Wheel lifted and grounded identification for an automotive vehicle

ABSTRACT

A control system ( 18 ) for an automotive vehicle ( 10 ) has a first roll condition detector ( 64 A), a second roll condition detector ( 64 B), a third roll condition detector ( 64 C), and a controller ( 26 ) that uses the roll condition generated by the roll condition detectors ( 64 A-C) to determine a wheel lift condition. Other roll condition detectors may also be used in the wheel lift determination. The wheel lift conditions may be active or passive or both.

RELATED APPLICATIONS

[0001] The present invention claims priority to U.S. provisional patentapplication Nos. 60/400,375, 60/400,261, 60/400,172, 60/400,376,60/400,156, and 60/400,155, all filed on Aug. 1, 2002, and No.60/401,418 filed on Aug. 5, 2002, and is a continuation-in-part of U.S.patent application Ser. No. 10/038,364 entitled “Wheel LiftIdentification For An Automotive Vehicle”, which is acontinuation-in-part of U.S. patent application Ser. No. 09/669,513entitled “Wheel Lift Identification For An Automotive Vehicle”, each ofwhich are hereby incorporated by reference herein, and U.S. patentapplications (Attorney Docket Nos. 202-0762/FGT-1678, 202-0634/FGT-1679,and 203-0670/FGT-1846), filed simultaneously herewith.

TECHNICAL FIELD

[0002] The present embodiment relates generally to a control apparatusfor controlling a system of an automotive vehicle in response to senseddynamic behavior, and more specifically, to a method and apparatus fordetermining whether a wheel of an automotive vehicle has lifted from thepavement using passive wheel lift detection.

BACKGROUND

[0003] Dynamic control systems for automotive vehicles have recentlybegun to be offered on various products. Dynamic control systemstypically control the yaw of the vehicle by controlling the brakingeffort at the various wheels of the vehicle. Yaw control systemstypically compare the desired direction of the vehicle based upon thesteering wheel angle and the direction of travel. By regulating theamount of braking at each corner of the vehicle, the desired directionof travel may be maintained. Typically, the dynamic control systems donot address rollover (wheels lifting) of the vehicle. For high profilevehicles in particular, it would be desirable to control the rollovercharacteristic of the vehicle to maintain the vehicle position withrespect to the road. That is, it is desirable to maintain contact ofeach of the four tires of the vehicle on the road.

[0004] In vehicle rollover control, it is desired to alter the vehicleattitude such that its motion along the roll direction is prevented fromachieving a predetermined limit (rollover limit) with the aid of theactuation from the available active systems such as controllable brakesystem, steering system and suspension system. Although the vehicleattitude is well defined, direct measurement is usually impossible.

[0005] During a potential vehicular rollover event, wheels on one sideof the vehicle start lifting, and the roll center of the vehicle shiftsto the contact patch of the remaining tires. This shifted roll centerincreases the roll moment of inertia of the vehicle, and hence reducesthe roll acceleration of the vehicle. However, the roll attitude couldstill increase rapidly. The corresponding roll motion when the vehiclestarts side lifting deviates from the roll motion during normal drivingconditions.

[0006] When the wheels start to lift from the pavement, it is desirableto confirm this condition. This allows the system to make an accuratedetermination as to the appropriate correction. If wheels are on theground, or recontact the ground after a lift condition, this alsoassists with accurate control.

[0007] Some systems use position sensors to measure the relativedistance between the vehicle body and the vehicle suspension. Onedrawback to such systems is that the distance from the body to the roadmust be inferred. This also increases the number of sensors on thevehicle. Other techniques use sensor signals to indirectly detect wheellifting qualitatively.

[0008] One example of a wheel lifting determination can be found in U.S.Pat. No. 6,356,188. The system applies a change in torque to the wheelsto determine wheel lift. The output from such a wheel liftingdetermination unit can be used qualitatively. This method is an activedetermination since the basis of the system relies on changing thetorque of the wheels by the application of brakes or the like. In somesituations it may be desirable to determine wheel lift without changingthe torque of a wheel.

[0009] It would therefore be desirable to provide a rollover detectionsystem that improves reliability in predicting the occurrence of wheellift during the operation of the automotive vehicle.

SUMMARY

[0010] It is therefore one object of the invention to provide a rolloverdetection system that may be used in conjunction with the dynamicstability control system of the vehicle to determine the presence of apotential rollover. The present invention seeks to determine the rollcondition and wheel lifting in a number of ways using the sensorsavailable from the vehicle control system. The various roll conditionsare compared to roll thresholds to determine the likelihood that thewheel has lifted. The control system then can make a determination as tohow to command the appropriate actuators to correct the potentialrollover condition.

[0011] In one aspect of the invention, a wheel lift identificationsystem for an automotive vehicle includes a first roll conditiondetector, a second roll condition detector, and a third roll conditiondetector. A controller determines wheel lift in response to the first,second, and third roll conditions.

[0012] In a further aspect of the invention, a method of controlling avehicle having a plurality of wheels comprises determining a relativeroll angle, determining a wheel departure angle, determining a rollingradius-based wheel departure angle, determining normal loading at eachwheel, determining an actual road torque, determining a wheellongitudinal slip; and determining a wheel lift status for saidplurality of wheels in response to said relative roll angle, said wheeldeparture angle, said rolling radius-based wheel departure roll angle,the normal loading at each wheel, an actual road torque and the wheellongitudinal slip.

[0013] One advantage of the invention is that by providing such a systeman improved determination of wheel lifting may be determined. Theaccuracy of the roll angle calculation may correspondingly be increased,resulting in a more appropriate braking or steering evasive action.

[0014] Other advantages and features of the present invention willbecome apparent when viewed in light of the detailed description of thepreferred embodiment when taken in conjunction with the attacheddrawings and appended claims.

BRIEF DESCRIPTION OF THE DRAWINGS

[0015]FIG. 1 is a diagrammatic view of a vehicle with variable vectorsand coordinate frames according to one embodiment of the presentinvention.

[0016]FIG. 2A is a block diagram of a stability system according to oneembodiment of the present invention.

[0017]FIG. 2B is a block diagrammatic view of the wheel lift detectionsystem of FIG. 2A.

[0018]FIG. 2C is a block diagrammatic view of the rollover stabilitycontrol feedback command of FIG. 2A.

[0019]FIG. 3 is a diagrammatic view of a vehicle showing thedisplacement of the vehicle body and axle relative to road surface.

[0020]FIG. 4 is a diagrammatic view showing the forces applied to thefront wheel/tire/suspension assembly during a potential rollover event.

[0021]FIG. 5 is a diagrammatic view showing the forces applied to therear wheel/tire/suspension assembly during a potential rollover event.

[0022]FIG. 6 is flow chart of a passive wheel lift determinationaccording to one embodiment of the present invention.

[0023]FIG. 7 is a flow chart of an active wheel lift identificationsystem according to one embodiment of the present invention.

[0024]FIG. 8A is a plot of pressure versus time for a wheel liftidentification system according to one embodiment of the presentinvention.

[0025]FIG. 8B is a plot of wheel speed versus time for a wheel liftidentification system according to one embodiment of the presentinvention.

[0026]FIG. 9 is a flow chart illustrating a plot of a passive wheel liftdetection using the operating torque of the vehicle.

[0027]FIG. 10 is an end view of an automotive vehicle on a bank.

[0028]FIG. 11 is a block diagrammatic view of the controller.

[0029]FIG. 12 is a high level flow chart illustrating conditiondetection and the resulting actions.

[0030]FIG. 13 is a flow chart of a drive train based decision step 302of FIG. 12.

[0031]FIG. 14 is a flow chart of the passive wheel lift groundingdetection step 304 of FIG. 12.

[0032]FIG. 15 is a flow chart of the active wheel lift groundingdetection step 308 of FIG. 12.

[0033]FIG. 16 is a flow chart of the resulting actions step 312 of FIG.12.

DETAILED DESCRIPTION

[0034] In the following figures the same reference numerals will be usedto identify the same components. The present invention may used inconjunction with a rollover control system for a vehicle. However, thepresent embodiment may also be used with a deployment device such asairbag or roll bar. The present invention will be discussed below interms of preferred embodiments relating to an automotive vehicle movingin a three-dimensional road terrain.

[0035] Wheel lift detection is the determination of when a wheel haslifted from the pavement. A passive system determines wheel liftindirectly using outputs from various sensors without perturbing thevehicle or wheels.

[0036] One aspect of the invention is passive wheel detection which isnamed in comparison with the so-called active wheel lift detection ofU.S. Pat. No. 6,356,188. In active wheel lift detection, the wheellifting is identified by requesting a change in torque at a wheel suchas by applying a small amount of pressure in each wheel and thenchecking what the wheel slip ratio is doing. In passive wheel liftdetection as set forth herein, the available sensor signals are used toidentify wheel lifting without the system requiring a pressure commandto the brake system of each wheel. Of course, as will be describedbelow, active and passive detection may be used together. Wheel liftingtypically occurs on the wheels on the inside of a turn. Depending on thevehicle configuration such as suspension, the front wheel or rear wheelmay lift first.

[0037] Another aspect includes active and passive and yet anotherincludes roll angle correction in response to wheel lift grounding.

[0038] Referring to FIG. 1, an automotive vehicle 10 with a safetysystem of the present invention is illustrated with the various forcesand moments thereon during a rollover condition. Vehicle 10 has frontright (FR) and front left (FL) wheel/tires 12A and 12B and rear right(RR) wheel/tires 13A and rear left (RL) tires 13B respectively. Thesetires are parenthetically identified 0, 1, 2, and 3 in some embodimentsbelow. The vehicle 10 may also have a number of different types of frontsteering systems 14 a and rear steering systems 14 b including havingeach of the front and rear wheels configured with a respectivecontrollable actuator, the front and rear wheels having a conventionaltype system in which both of the front wheels are controlled togetherand both of the rear wheels are controlled together, a system havingconventional front steering and independently controllable rear steeringfor each of the wheels or vice versa. Generally, the vehicle has aweight represented as Mg at the center of gravity of the vehicle, whereg=9.8 m/s² and M is the total mass of the vehicle.

[0039] As mentioned above, the system may also be used with safetysystems including active/semi-active suspension systems, anti-roll bar,or airbags or other safety devices deployed or activated upon sensingpredetermined dynamic conditions of the vehicle.

[0040] The sensing system 16 is coupled to a control system 18. Thesensing system 16 may comprise many different sensors including thesensor set typically found in a yaw control system (including lateralaccelerometer, yaw rate sensor, steering angle sensor and wheel speedsensors) together with a roll rate sensor, a vertical accelerometer, anda longitudinal accelerometer. The various sensors will be furtherdescribed below. The present embodiment uses the various sensors todetermine wheel lift. The sensors may also be used by the control systemin various determinations such as to determine a lifting event. Thewheel speed sensors 20 are mounted at each corner of the vehicle andgenerate signals corresponding to the rotational speed of each wheel.The rest of the sensors of sensing system 16 may be mounted directly onthe center of gravity of the vehicle body, along the directions x, y andz shown in FIG. 1. As those skilled in the art will recognize, the framefrom b₁, b₂ and b₃ is called a body frame 22, whose origin is located atthe center of gravity of the car body, with the b₁ corresponding to thex axis pointing forward, b₂ corresponding to the y axis pointing off thedriving side (to the left), and the b₃ corresponding to the z axispointing upward. The angular rates of the car body are denoted abouttheir respective axes as ω_(x) for the roll rate, ω_(y) for the pitchrate and ω_(z) for the yaw rate. The calculations may take place in aninertial frame 24 that may be derived from the body frame 22 asdescribed below.

[0041] The angular rate sensors and the accelerometers may be mounted onthe vehicle car body along the body frame directions b₁, b₂ and b₃,which are the x-y-z axes of the sprung mass of the vehicle.

[0042] The longitudinal acceleration sensor is mounted on the car bodylocated at the center of gravity, with its sensing direction alongb₁-axis, whose output is denoted as α_(x). The lateral accelerationsensor is mounted on the car body and may be located at the center ofgravity, with its sensing direction along b₂-axis, whose output isdenoted as α_(y).

[0043] The other frame used in the following discussion includes theroad frame, as depicted in FIG. 1. The road frame system r₁r₂r₃ is fixedon the driven road surface, where the r₃ axis is along the average roadnormal direction computed from the normal directions of thefour-tire/road contact patches.

[0044] In the following discussion, the Euler angles of the body frameb₁b₂b₃ with respect to the road frame r₁r₂r₃ are denoted as θ_(xbr),θ_(ybr) and θ_(zbr), which are also called the relative Euler angles(i.e., relative roll, relative pitch and relative yaw angles,respectively).

[0045] Referring now to FIG. 2, roll stability control system 18 isillustrated in further detail having a controller 26 used for receivinginformation from a number of sensors which may include a yaw rate sensor28, a speed sensor 20, a lateral acceleration sensor 32, a verticalacceleration sensor 33, a roll angular rate sensor 34, a steering wheel(hand wheel) angle sensor 35, a longitudinal acceleration sensor 36, apitch rate sensor 37, steering angle (of the wheels or actuator)position sensor 38, suspension load sensor 40 and suspension positionsensor 42.

[0046] Controller 26 may include a signal multiplexer 50 that is used toreceive the signals from the sensors 28-42. The signal multiplexer 50provides the signals to a wheel lift detector 52, a vehicle roll anglecalculator 54, and to a roll stability control (RSC) feedback controlcommand 56. Also, wheel lift detector 52 may be coupled to the vehicleroll angle calculator 54. The vehicle roll angle calculator 54 may alsobe coupled to the RSC feedback command 56. Vehicle roll angle calculator54 is described in provisional application Nos. 60/400,376 and60/400,172, and U.S. application (Docket No. 201-0938/FGT 1660), thedisclosures of which are incorporated herein by reference.

[0047] Referring now also to FIG. 2B, the wheel lift detector 52 mayinclude passive wheel detector 58 as will be further described herein,active wheel detector 60 as described above with respect to the priorart and an integrated wheel lift detector 62. Thus, both active andpassive may be used together. As will be further described below, anarbitration scheme between the active and passive lifting may be used ina wheel final lift determination within the integrated wheel liftdetector 62.

[0048] Referring now also to FIG. 2C, the roll stability control (RSC)controller 26 may also include a first roll condition detector 64A, asecond roll condition detector 64B, a third roll condition detector 64C,a fourth roll condition detector 64D, and a roll event sensor 66. Itshould be noted that the implementation of the wheel lift detector 52,the vehicle roll angle calculator 54, the roll stability controlfeedback control command 56 having a torque control system 57 (describedfurther below), the passive wheel lift detection 58, the active wheellift detection 60, and the integrated wheel lift detection 62 may all beincorporated in software within the controller 26. Separate controldevices may also be used.

[0049] Wheel lift detector 52 determines a qualitative determination ofvehicle rollover. This is in contrast to the vehicle roll anglecalculator 54, which is a quantitative determination of rollover. Activewheel lift detector 60 can be determined in many ways including U.S.Provisional Application Nos. 60/400,375 and 60/400,156, both filed Aug.1, 2002, and U.S. Pat. No. 6,356,188, the disclosures of which areincorporated by reference herein. The integrated wheel lift detector 62is set forth in U.S. Provisional Application No. 60/401,418 filed Aug.5, 2002, the disclosure of which is incorporated herein. Vehicle rollangle calculator 54 is described in U.S. Provisional Application Nos.60/400,376 and 60/400,172, both filed Aug. 1, 2002, and Ford Disclosure201-0938 (FGT 1660), which are incorporated by reference herein.

[0050] In the preferred embodiment the sensors are located at the centerof gravity of the vehicle. Those skilled in the art will recognize thatthe sensor may also be located off the center of gravity and translatedequivalently thereto.

[0051] Lateral acceleration, roll orientation and speed may be obtainedusing a global positioning system (GPS). Based upon inputs from thesensors, controller 26 may control a safety device 44. Depending on thedesired sensitivity of the system and various other factors, not all thesensors 28-42 may be used in a commercial embodiment. Safety device 44may control an airbag 45 or a steering actuator/braking actuator 46A-Dat one or more of the wheels 12A, 12B, 13A, 13B of the vehicle. Also,other vehicle components such as a suspension control 48 may be used toadjust the suspension to prevent rollover.

[0052] Roll angular rate sensor 34 and pitch rate sensor 37 may sensethe roll condition or lifting of the vehicle based on sensing the heightof one or more points on the vehicle relative to the road surface.Sensors that may be used to achieve this include a radar-based proximitysensor, a laser-based proximity sensor and a sonar-based proximitysensor.

[0053] Roll rate sensor 34 and pitch rate sensor 37 may also sense theroll condition or lifting based on sensing the linear or rotationalrelative displacement or displacement velocity of one or more of thesuspension chassis components. This may be in addition to or incombination with suspension position sensor 42. The position sensor 42,roll rate sensor 34 and/or the pitch rate sensor 37 may include a linearheight or travel sensor, a rotary height or travel sensor, a wheel speedsensor used to look for a change in velocity, a steering wheel positionsensor, a steering wheel velocity sensor and a driver heading commandinput from an electronic component that may include steer by wire usinga hand wheel or joy stick.

[0054] The roll condition or lifting may also be sensed by sensingdirectly or estimating the force or torque associated with the loadingcondition of one or more suspension or chassis components including apressure transducer in an air suspension, a shock absorber sensor suchas a load sensor 40, a strain gauge, the steering system absolute orrelative motor load, the steering system pressure of the hydrauliclines, a tire lateral force sensor or sensors, a longitudinal tire forcesensor, a vertical tire force sensor or a tire sidewall torsion sensor.The yaw rate sensor 28, the roll rate sensor 34, the lateralacceleration sensor 32, and the longitudinal acceleration sensor 36 maybe used together to determine that the wheel has lifted. Such sensorsmay be used to determine wheel lift or estimate normal loadingassociated with wheel lift. These are passive methods as well.

[0055] The roll condition of the vehicle may also be established by oneor more of the following translational or rotational positions,velocities or accelerations of the vehicle including a roll gyro, theroll rate sensor 34, the yaw rate sensor 28, the lateral accelerationsensor 32, the vertical acceleration sensor 33, a vehicle longitudinalacceleration sensor 36, lateral or vertical speed sensor including awheel-based speed sensor 20, a radar-based speed sensor, a sonar-basedspeed sensor, a laser-based speed sensor or an optical-based speedsensor.

[0056] Safety device 44 may control the position of the front rightwheel actuator 46A, the front left wheel actuator 46B, the rear leftwheel actuator 46C, and the right rear wheel actuator 46D. Although asdescribed above, two or more of the actuators may be simultaneouslycontrolled. For example, in a rack-and-pinion system, the two wheelscoupled thereto are simultaneously controlled. Based on the inputs fromsensors 28 through 42, controller 0.26 determines a roll conditionand/or wheel lift and controls the steering position of the wheels.

[0057] Speed sensor 20 may be one of a variety of speed sensors known tothose skilled in the art. For example, a suitable speed sensor mayinclude a sensor at every wheel that is averaged by controller 26. Thecontroller may translate the wheel speeds into the speed of the vehicle.Yaw rate, steering angle, wheel speed and possibly a slip angle estimateat each wheel may be translated back to the speed of the vehicle at thecenter of gravity. Various other algorithms are known to those skilledin the art. Speed may also be obtained from a transmission sensor. Forexample, if speed is determined while speeding up or braking around acorner, the lowest or highest wheel speed may not be used because of itserror. Also, a transmission sensor may be used to determine vehiclespeed.

[0058] Load sensor 40 may be a load cell coupled to one or moresuspension components. By measuring the stress, strain or weight on theload sensor a shifting of the load can be determined.

[0059] Several different combinations of sensors may be used todetermine a wheel lift status. Once the qualitative wheel lift isdetermined, quantitative roll condition may be determined. The followingis a summary of how the quantitative wheel lifting indication from thevarious vehicle motion variables after qualitative wheel lifting statusis identified.

[0060] The roll condition of a vehicle can be characterized by therelative roll angle between the vehicle body and the wheel axle and thewheel departure angle (between the wheel axle and the average roadsurface). Both the relative roll angle and the wheel departure angle maybe calculated in relative roll angle estimation module by using the rollrate and lateral acceleration sensor signals. If both the relative rollangle and the wheel departure angles are large enough, the vehicle maybe in either single wheel lifting or double wheel lifting. On the otherhand, if the magnitude of both angles are small enough, the wheels arelikely all grounded.

[0061] The roll condition of a vehicle can be characterized by rollingradius-based wheel departure roll angle, which captures the anglebetween the wheel axle and the average road surface through the dynamicrolling radii of the left and right wheels when both of the wheels aregrounded. Since the computation of the rolling radius is related to thewheel speed and the linear velocity of the wheel, such rolling-radiusbased wheel departure angle will assume abnormal values when there arelarge wheel slips. This happens when a wheel is lifted and there istorque applied to the wheel. Therefore, if this rolling radius-basedwheel departure angle is increasing rapidly, the vehicle might havelifted wheels. Small magnitude of this angle indicates the wheels areall grounded.

[0062] The roll condition of the vehicle can be seen indirectly from thewheel longitudinal slip. If during a normal braking or driving torquethe wheels at one side of the vehicle experience increased magnitude ofslip, then the wheels of that side are losing longitudinal road torque.This implies that the wheels are either driven on a low mu surface orlifted up.

[0063] The roll condition of the vehicle can be characterized by thenormal loading sustained at each wheel. Theoretically, when a normalloading at a wheel decreases to zero, the wheel is no longer contactingthe road surface. In this case a potential rollover is under the way.Large magnitude of this loading indicates that the wheel is grounded.

[0064] The roll condition can be identified by checking the actual roadtorques applied to the wheels and the road torques which are needed tosustain the wheels when they are grounded. The actual road torques canbe obtained through torque balancing for each wheel using wheelacceleration, driving torque and braking torque. If the wheel iscontacting the road surface, the calculated actual road torques mustmatch or be larger than the nonlinear torques calculated from the normalloading and the longitudinal slip at each wheel.

Relative Roll Angle and Wheel Departure Angle Using Lateral Accelerationand Roll Angular Rate Sensor

[0065] The roll condition of a vehicle can be characterized by therelative roll angle θ_(xr) between the vehicle body and the wheel axle,which has been calculated by using the roll rate and lateralacceleration sensor signals. If this roll angle is increasing rapidly,the vehicle might be in the edge of wheel lifting or rollover. Smallmagnitude of this angle indicates the wheels are not lifted or are allgrounded.

[0066] The roll condition of a vehicle can also be characterized by theroll angle between the wheel axle and the average road surface, this iscalled wheel departure angle. If this roll angle is increasing rapidly,the vehicle has lifted wheel or wheels and aggressive control actionneeds to be taken in order to prevent the vehicle from rolling over.Small magnitude of this angle indicates the wheels are not lifted. Thissection describes how to quantitatively determine the vehicle roll anglewhen a qualitative wheel lifting is identified. That is, if aqualitative wheel lifting is detected, a quantitative computation of thewheel lifting may be initiated.

[0067] Referring now to FIGS. 3, 4 and 5, the present invention will bediscussed below in terms of preferred embodiments relating to anautomotive vehicle having a wheel/tire/suspension assembly 354 duringpotential rollover events where one side of the vehicle is lifted orwheels on one side of the vehicle lose contact with the road surface orwheels on one side do not carry normal loadings. Thewheel/tire/suspension assembly has an axle 356. Although a physical axlemay not be present, axle is a term used for the common axis of the frontor rear wheels.

[0068] The sensing system uses the lateral acceleration sensor 32 andthe roll angular rate sensor 34 to determine wheel lift in one of theroll condition detectors 64A-D. The lateral acceleration sensor 32 isused to measure the total lateral acceleration of the center of gravityof the vehicle body, and the roll rate sensor 34 measures the vehiclebody roll angular rate. The method of determining wheel lifting usingthe roll rate sensor 34 and the lateral acceleration sensor 32 isdescribed in U.S. patent application (Docket Number 201-0938/FGT 1660),the disclosure of which is incorporated by reference.

[0069] The vehicle body 10 is connected with the wheel/tire assemblies12A, 12B, 13A, 13B through suspensions 360 _(lr), 360 _(rr), 360 _(lf),and 360 _(rf), collectively suspension 360. The tire forces aretransferred to the vehicle body through the suspensions 360. Thoseforces can be projected along the vehicle body-fixed y- and z-axes. Thesuspension forces projected along the body-fixed y axis (or body-fixedlateral direction) are denoted as S_(ylf), S_(yrf), S_(ylr), S_(yrr) atthe left-front, right-front, left-rear and right-rear corners; thesuspension forces projected along the body-fixed z axis (or body-fixedvertical direction) as S_(zlf), S_(zrf), S_(zlr), S_(zrr). The totallateral forces applied to the vehicle body along the body-fixed lateralaxis are S_(y), i.e.

S _(y) =S _(ylf) +S _(yrf) +S _(ylr) +S _(yrr)  (1)

[0070] The vehicle body has roll angular displacement due to thesuspension forces and the vehicle roll accelerations. The roll angularrate of the vehicle body is ω_(x). Around center of gravity of thevehicle body, the suspension forces-induced roll moment around thevehicle center of gravity (c.g.) needs to match the inertia moment fromthis ω_(x). The suspension forces-induced roll moment around the c.g.has two terms:

[0071] the roll moment M_(susp-vert) due to the vertical suspensionforces S_(zlf), S_(zrf), S_(zlr), S_(zrr);

[0072] the roll moment M_(susp-lat) due to the total lateral suspensionforce S_(y).

[0073] From FIG. 5, the following expressions for M_(susp-vert) andM_(susp-lat) may be obtained

M _(susp-vert)=(S _(zrf) −S _(zlf) +S _(zrr) −S _(zir))l

M _(susp-lat) =S _(y) h _(cg).  (2)

[0074] The vehicle body roll angular rate must satisfy the following

I _(x){dot over (ω)}_(x) =M _(susp-vert) +M _(susp-lat)  (3)

[0075] where I_(x) is the vehicle body roll moment of inertia around thec.g. of the vehicle body. If the suspension resultant roll stiffness androll damping rates (including anti-roll-bars, suspensions, etc.) arerespectively defined as K_(roll) and D_(roll), and θ_(bw) as therelative angular displacement between the vehicle body and the averagewheel axle, then the roll moment due to vertical suspension forcesM_(susp-vert) can be further expressed as

M _(susp-vert) =−K _(roll)θ_(bw) −D _(roll){dot over (θ)}_(bw).  (4)

[0076] The roll moment due to lateral suspension forces M_(susp-lat)needs to be further defined so that the roll angular rate sensors andthe lateral accelerometer may be used. The longitudinal and lateralvelocities of the c.g. of the vehicle body are ν_(z) and ν_(y), whichare measured along body-fixed x- and y-axis respectively, and ω_(z) isthe yaw rate of the vehicle. The lateral dynamics of the vehicle bodywill satisfy the following equation of motion based on Newton's law:

M _(s)({dot over (ν)}_(y)+ω_(z)ν_(x))=S _(y) +M _(s) gsin(θ_(bw)+θ_(wr))  (5)

[0077] where θ_(wr) is the relative angular displacement between thewheel axle and the road surface, (or the departure angle of the wheelaxle from the road surface), M_(s) is the vehicle body mass (or thesprung mass of the vehicle). Solving S_(y) from (5) and substitutingS_(y) into the second equation of (2) leads to

M _(susp-lat) +M _(s)({dot over (ν)}_(y)+ω_(z)ν_(x))h _(cg) −M _(s) gsin(θ_(bw)+θ_(wr))h _(cg).  (6)

[0078] The dynamic equation to depict the wheel axle departure anglefrom the road surface. There are two wheel sets, one on the front (FIG.4) and one on the rear (FIG. 5). Due to the differences in front andrear suspensions and inertias, there are slight differences between thefront and the rear wheel axle departure angles. θ_(wr-front) is denotedas the front wheel departure angle and θ_(wr-rear) is denoted as therear wheel departure angle. The average of those two angles is used todefine the angle θ_(wr) $\begin{matrix}{\theta_{wr} = {\frac{\theta_{{wr} - {front}} + \theta_{{wr} - {rear}}}{2}.}} & (7)\end{matrix}$

[0079] The assembly consists of the wheel, the tires and thesuspensions. FIG. 5 shows the rear axle of such assembly. In order toavoid solving the front lateral and vertical tire forces F_(yf) andF_(zf), the rear lateral and vertical tire forces F_(yr) and F_(zr), theequation of motion was written around the outer tire contact patch forfront and rear assemblies

I _(wxf){umlaut over (θ)}_(wr)=(h−h _(cg))cos(θ_(bw))[S _(ylf) +S _(yrf)]−M _(uf) gl _(w) cos(θ_(wr))+(S _(zlf) −S _(zrf))l

I _(wxr){umlaut over (θ)}_(wr)=(h−h _(cg))cos(θ_(bw))[S _(ylr) +S _(yrr)]−M _(ur) gl _(w) cos(θ_(wr))+(S _(zlr) −S _(zrr))l  (8)

[0080] where h_(cg) is the distance between the vehicle body c.g. andthe road surface when the car is parked; I_(wxf) and I_(wxr) are theroll moments of inertia of the front and rear wheel/tire/suspensionassemblies around the contact patches of the outer tires; M_(uf) andM_(ur) are the total masses of the front and rear wheel/tire/suspensionassemblies; l_(w) is the half of the wheel track.

[0081] Up to now, vehicle states or motion variables were associatedwith the relative roll angles of interest. The goal is to determine therelative roll angles with the available sensor signals. In order toestablish the connection, the sensor signals are related with thosemotion variables used to derive equations (3) and (8). First considerthe lateral acceleration sensor output, which is denoted asα_(y-sensor). The measured signal α_(y-sensor) includes variouscomponents due to the vehicle yaw, longitudinal, lateral motions andgravity, and it can be related to the lateral, longitudinal, yaw motionvariables and the gravity, as in the following:

α_(y-sensor)=ν_(y)+ω_(z)ν_(x) −g sin(θ_(bw) +θ _(wr))  (9)

[0082] and the roll angular rate sensor output measures the same rollrate used before, i.e.,

ω_(x-sensor)=ω_(x).  (10)

[0083] Substituting (9) into (5) leads to

M _(susp-lat) =M _(s) h _(cg)α_(y-sensor)

S _(y) =M _(s)α_(y-sensor).  (11)

[0084] Therefore (3) can be simplified into

{dot over (θ)}_(bw) =−c ₁θ_(bw) −c ₂{dot over (ω)}_(x-sensor) +c₃α_(y-sensor)  (12)

[0085] where the coefficients in the equation can be related to thevehicle parameters as in the following:${c_{1} = \frac{K_{roll}}{D_{roll}}},\quad {c_{2} = \frac{I_{x}}{D_{roll}}},\quad {c_{3} = {\frac{M_{s}h_{cg}}{D_{roll}}.}}$

[0086] Adding together the two equations in (8) and Substituting (11)into the resultant equation leads to the following equation

{umlaut over (θ)}_(wr) =−d ₁ cos(θ_(wr))+d ₂α_(y-sensor) cos(θ_(bw))+d₃θ_(bw) +d ₄{dot over (θ)}_(bw)  (13)

[0087] where the coefficients in the equation can be related to thevehicle parameters as${d_{1} = {\frac{\left( {M_{uf} + M_{ur}} \right)l_{w}}{I_{wxf} + I_{wxr}}g}},\quad {d_{2} = \frac{M_{s}\left( {h - h_{cg}} \right)}{I_{wxf} + I_{wxr}}},{d_{3} = \frac{K_{roll}}{I_{wxf} + I_{wxr}}},\quad {d_{4} = {\frac{D_{roll}}{I_{wxf} + I_{wxr}}.}}$

[0088] Based on (12) and, the angles of interests can be related to thetwo sensor signals α_(y-sensor) and ω_(x)-sensor A digital algorithmusing a Tyler expansion to the continuous time differential equation inorder to obtain the digital version of the sensing algorithm can be usedas in the following for estimating the relative roll angles

θ_(bw)(k+1)=θ_(bw)(k)+ΔT*f(k)

x(k+1)=x(k)+ΔT*g(k)

θ_(wr)(k+1)=θ_(wr)(k)+ΔT*x(k)+ΔT ² *g(k)  (14)

[0089] where ΔT is the sampling time of the implemented algorithm,

f(k)=−c ₁θ_(bw)(k)−c ₂ω_(x-sensor)(k)+c ₃α_(y-sensor)(k)

g(k)=−d ₁ cos(θ_(wr)(k))+d ₂α_(y-sensor)(k)cos(θ_(bw)(k))+d ₃θ_(bw)(k)+d₄θ_(bw)(k).  (15)

[0090] In a digital implementation, the previously known angles areiteratively used in the angle determinations. This reduces the over allnumber of processing steps which leads to faster results and ultimatelythose angles add more control authority to the potential vehiclerollover event.

[0091] Since the quantitative determination of the wheel departure angleas in (14) depends on when the computation should be started, aqualitative rollover indication is required. One of such qualitativerollover indication is the wheel lifting detection. Thus, based on thewheel lifting status using the method proposed in this disclosure, aquantitative determination of how large the wheel lift is may bedetermined, which can be used to generate brake control command.

Rolling Radius-Based Wheel Departure Roll Angle, θ_(r-whl)

[0092] Based on the rolling radius-based wheel departure angle, a firstqualitative indication of wheel lifting may be made as one of the rollcondition detectors 64. The rolling radius r(i) of the i-th rollingwheel of a moving vehicle is related to the i-th wheel speed w_(i).(from the i-th ABS wheel speed sensor) and the linear corner velocity ofthe wheel ν_(c)(i) (calculated from the steering angle, the side slipangle and the reference velocity of the vehicle) in the followingequation: $\begin{matrix}{{r(i)} = \frac{{v_{c}(i)}{R(i)}}{w(i)}} & (16)\end{matrix}$

[0093] where i=0, 1, 2, 3 implies the front-left, front-right, rear-leftand rear-right wheel, and R(i) is the nominal rolling radius used toconvert the rotational speed of each wheel to a linear speed. UsuallyR(0)=R(1)=R_(f) for front wheels and R(2)=R(3)=R_(r) for rear wheels, orR(0)=R(1)=R(2)=R(3)=R₀.

[0094] The linear corner velocity is derived from the followingequation:

ν_(c)(0)=V _(x)[ cos(δ)+tan(β)sin(δ)]+ω_(z) [l _(f) sin(δ)−t _(f)cos(δ)]

ν_(c)(1)=V _(x)[ cos(δ)+tan(β)sin(δ)]+ω_(z) [l _(f) sin(δ)+t _(f)cos(δ)]

ν_(c)(2)=V _(x) −ω _(z) t _(r)

ν_(c)(3)=V _(x) +ω _(z) t _(r)  (16.5)

[0095] where t_(f) and t_(r) are the half tracks for the front and rearaxles, l_(f) and l_(r) are the distances between the center of gravityof the vehicle and the front and rear axles, δ is the steering angle atthe front wheel, β is the side slip angle of the vehicle, ω_(z) is theyaw rate of the vehicle.

[0096] The front axle rolling radii-based wheel departure angleθ_(rr-whl)(0) can be computed from the rolling radii of the front-leftand front-right rolling radii in the equation $\begin{matrix}{{\theta_{{rr} - {whl}}(0)} = {\tan^{- 1}\left\lbrack \frac{{r(0)} - {r(1)}}{t_{f}} \right\rbrack}} & (17)\end{matrix}$

[0097] and the rear axle rolling radii-wheel departure angleθ_(rr-whl)(1) may be calculated from the following equation$\begin{matrix}{{\theta_{{rr} - {whl}}(1)} = {\tan^{- 1}\left\lbrack \frac{{r(2)} - {r(3)}}{t_{r}} \right\rbrack}} & (18)\end{matrix}$

[0098] where t_(f) is the width of the front wheel track and t_(r) isthe rear wheel track. Axle refers to a common axis not necessarily afixed or physical axle. Using formula (16), (17) and (18), the anglesθ_(rr-whl)(0) and θ_(rr-whl)(1) can be computed as in the following ifv_(ref) > 5 for (i = 0;i < 4; ++)$\left\{ \quad {{{r(i)} = {{sat}\left( {\frac{{v_{c}(i)}R_{0}}{\max \left( {{w(i)},0.01} \right)},{{p\_ MAX}{\_ DRR}}} \right)}};}\quad \right\}$

$\begin{matrix}{{{\theta_{{rr} - {whl}}(0)} = {{sat}\left( {\frac{{r(0)} - {r(1)}}{t_{f}},{{p\_ MAX}{\_ WDA}}} \right)}};} \\{{{\theta_{{rr} - {whl}}(1)} = {{sat}\left( {\frac{{r(2)} - {r(3)}}{t_{f}},{{p\_ MAX}{\_ WDA}}} \right)}};}\end{matrix}\quad$

} else { θ_(rr−whl)(0) = 0; θ_(rr−whl)(1) = 0; }

[0099] where p_MAX_DRR (for example, 1000) is the allowed maximumdynamic rolling radius, and p_MAX_WDA (for example, 13 degree) is themaximum rolling radius based wheel departure angle.

[0100] Notice that the above deviation assumes that the wheel hasnegative slip, i.e., there are braking torques applied to the wheels. Inthe case there are positive torques applied to the wheels, a negativesign is needed. The system is passive in a sense that a change in torqueis not purposely applied as an active actuator command and it is aquantity passively received or observed. That is, the engine operatinginput torque is used. if (τ_(active)(0) > 0 & & τ_(active)(1) > 0) {θ_(rr-whl)(0) = −θ_(rr-whl)(0); } if (τ_(active)(2) > 0 & &τ_(active)(3) > 0) { θ_(rr-whl)(1) = −θ_(rr-whl)(1); }

[0101] where τ_(active)(i) denotes the observed torque applied to theith wheel, which could be either a driving torque or a braking torque,or say τ_(active)(i)=τ_(driving)(i)−τ_(braking)(i).

[0102] Notice that the above computation provides accurate captures forthe front and rear wheel axle departure angle if the involved two wheelshave zero or small longitudinal slip ratio (by comparing a calculatedlongitudinal slip ratio to a longitudinal slip ratio threshold. In thecase when a large wheel longitudinal slip is experienced, theafore-mentioned computations are no longer very accurate. However, theymay still be used to identify a significant slip difference between leftand right wheels. If one of the involved wheels has large slip ratio(for example, its wheel speed is close to zero), the computation of (17)or (18) will amplify the wheel departure angle (very large wheeldeparture angle up to 90 degree, this is not the true wheel departureangle). If both the involved wheels have the similar but large slipratios, (17) or (18) will still be small, implying grounded wheels forboth left and right sides.

[0103] Thus, the computation as in (17) or (18) provides accuratedescription of wheel departure angle (wheel roll angle) from the averageroad surface if the wheels do not experience large longitudinal slip; itprovides amplified characterization when the involved left and rightwheels have significant slip differences.

Longitudinal Wheel Slip Ratio

[0104] Another way in which to passively detect wheel lift in one of theroll condition detectors 64 uses longitudinal wheel slip ratio.Longitudinal wheel slip may be used to generate a second qualitativeindication of wheel lift.

[0105] The slip power is defined as the product of the slip ratio andthe time derivative of the slip ratio. The longitudinal slip ratio isthe ratio of the$\frac{{wheel}\quad {speed}}{{vehicle}\quad {speed}} = {{vehicle}\quad {{speed}.}}$

[0106] The vehicle speed may be the vehicle speed vehicle speed at thecorner of the vehicle as described below. If the ith wheel slip isdenoted as s(i) for i—0, 1, 2, 3, then $\begin{matrix}{{s_{p}(i)} = {{s(i)}{\frac{{s(i)}}{t}.}}} & (19)\end{matrix}$

[0107] The calculated slip power s_(p) reflects the magnitude variationof the wheel slip ratio with respect to time $\begin{matrix}{{\frac{}{t}\left\lbrack {s(i)} \right\rbrack}^{2} = {{2{s(i)}\frac{{s(i)}}{t}} = {2{{s_{p}(i)}.}}}} & (20)\end{matrix}$

[0108] Therefore, positive slip power implies divergent wheel slip(magnitude of slip ratio is increased), negative slip power indicates aconvergent slip ratio (the magnitude of slip ratio is decreased), zeroslip power implies that the slip ratio is kept constant. Since duringwheel lifting, both braking torque and driving torque will generatedivergent slip for the wheel, hence positive slip power is expected.While in the case of wheel touch-down or a grounded wheel, convergentwheel slip (negative slip power) is expected. for (i = 0; i < 4; i + +){ ds(i) = p_10HZ_COEF * ds(i) + (s(i) − z1_s(i)) * (1 −p_10HZ_COEF)/0.007; z1_s(i) = s(i); }

[0109] where p_(—)10 HZ_COEF (for example, 0.9) is the coefficientreflecting a low-pass filter with 10 Hz cut-off frequency.

[0110] Thus, wheel slip power provides a real-time characterization ofthe trend of the wheel slips during transient wheel speed changes toprovide a qualitative indication of wheel lifting and thus a wheel liftsignal.

Slip Rate Wheel Lift

[0111] The roll condition or wheel lift of the vehicle can also be seenindirectly from the wheel longitudinal slip rate. If during a normalbraking or driving torque the wheels at one side of the vehicleexperience an increased magnitude of slip rate, then the wheels arelosing longitudinal road torque. This implies that the wheels are eitherdriven on a low mu surface or lifted up. Thus, the longitudinal sliprate s_(r) may be used in a determination of torque based qualitativedetermination of the wheel lifting.

[0112] The slip rate is defined as the product of the corner velocityand the time derivative of the slip ratio for the ith wheel, i.e.,$\begin{matrix}{{s_{r}(i)} = {{v_{c}(i)}{\frac{{s(i)}}{t}.}}} & (21)\end{matrix}$

[0113] Thus calculated slip rate is related to wheel acceleration$\begin{matrix}{{\frac{\quad}{t}{w(i)}} = {{\frac{\quad}{t}\left\{ {{v_{c}(i)}\left\lbrack {{s(i)} + 1} \right\rbrack} \right\}} = {{s_{r}(i)} + {\left\lbrack {{s(i)} + 1} \right\rbrack {\frac{{_{v_{c}}(i)}\quad}{t}.}}}}} & (22)\end{matrix}$

[0114] Considering corner velocity ν_(c)(i) is usually smooth, (22) canbe simplified to $\begin{matrix}{{\frac{\quad}{t}{w(i)}} \approx {{s_{r}(i)}.}} & (23)\end{matrix}$

[0115] Hence slip rate is a characterization of the wheel accelerationbut with computation advantage, i.e., smoothness. Notice that duringtransient wheel speed changes, (23) is very accurate due to the factthat the wheel acceleration magnitude is much larger than the magnitudeof the time derivative of the corner velocity. for (i = 0; i < 4; i + +){ s_(r)(i) = sat(v_(c)(i) * ds(i),−p_MAX_SLIP_RATE,p_MAX_SLIP_(—) RATE);}

[0116] where p_MAX_SLIP_RATE (for example, 300) is the upper bound forlimiting slip rate. Thus, as can be seen from the above formula, sliprate can be determined within bounds of the p_MAX_SLIP_RATE usingequation (21). The slip rate is compared to a threshold. If the sliprate increases above a slip rate threshold, then the wheel may bepossibly lifted.

[0117] As will be further described below, the calculated wheel sliprate may also be used to compute the actual torques applied to eachwheel.

Wheel Lift Using Normal Loading

[0118] The roll condition of the vehicle can also be characterized bythe normal loading sustained at each wheel. Theoretically, the normalloading of a wheel decreasing to or near zero indicates that the wheelis no longer contacting the road surface. In this case a potentialrollover is under the way. Large magnitude of this loading indicatesthat the wheel is grounded.

[0119] Normal loading is also used in a torque based wheel liftdetermination as described below. The normal loading as used herein isthe dynamic normal loading which is experienced by any of the fourwheels during vehicle dynamic maneuvers. Those normal loadings aremeasured along the normal directions of the contact patches, which arethe areas where the wheels and the road surface meets. If the vehicle isdriven on a level ground, then the normal loadings are located at thecontact patches between the road and the wheels, and are perpendicularto the road surface.

[0120] The defined dynamic normal loading of each wheel consists of twoportions: the portion due to the heave motion of the vehicle (denoted asN_(heave)) and the portion due to the other motions of the vehicle(denoted as N_(non-heave)). That is, the total normal loading at eachwheel (denoted as N_(total)) is the sum of N_(heave) and N_(non-heave).

[0121] The heave motion generated normal loading can be calculated asthe following $\begin{matrix}{{{N_{heave}(0)} = {{N_{heave}(1)} = {{Ma}_{z}\quad {\cos \left( \theta_{xr} \right)}\quad {\cos \left( \theta_{y\quad r} \right)}\frac{l_{r}}{2\left( {l_{f} + l_{r}} \right)}}}}{{N_{heave}(2)} = {{N_{heave}(3)} = {{Ma}_{z}\quad {\cos \left( \theta_{xr} \right)}\quad {\cos \left( \theta_{y\quad r} \right)}\frac{l_{f}}{2\left( {l_{f} + l_{r}} \right)}}}}} & (24)\end{matrix}$

[0122] where α_(z) is a vertical acceleration signal from the verticalacceleration sensor 33 that may be mounted on the vehicle body but atthe center of gravity of the vehicle; M is the total mass of thevehicle; θ_(xr) is the relative roll angle between the vehicle body andthe axle of the wheels that is derived from the roll rate sensor; θ_(yr)is the relative pitch angle between the vehicle body and the roadsurface that is derived from the pitch rate sensor; l_(f) is thedistance of the vehicle center of gravity from the front axle, and l_(r)is the distance of the vehicle center of gravity from the rear axle.

[0123] The non-heave motion portion of the normal loadings are due tothe other motion of the vehicle, including the roll and pitch angularmotion of the vehicle body with respect to the road surface, the loadtransfers due to the longitudinal and lateral accelerations, which canbe calculated as in the following

N _(non-heave)(0)=K _(f)(−θ_(xr) t _(f)+θ_(yr) l_(f))cos(θ_(xr))cos(θ_(yr))

N _(non-heave)(1)=K _(f)(θ_(xr) t _(f)+θ_(yr) l_(f))cos(θ_(xr))cos(θ_(yr))

N _(non-heave)(2)=K _(f)(−θ_(xr) t _(f)−θ_(yr) l_(f))cos(θ_(xr))cos(θ_(yr))

N _(non-heave)(3)=K _(f)(θ_(xr) t _(f)−θ_(yr) l_(f))cos(θ_(xr))cos(θ_(yr))  (25)

[0124] where K_(f) is the spring rate of the front suspensions and K_(r)is the spring rate of the rear suspensions.

[0125] Consequently, the total normal loadings at the wheels can beexpressed as the following $\begin{matrix}{{{N_{total}(0)} = {{{Ma}_{z}\quad {\cos \left( \theta_{xr} \right)}\quad {\cos \left( \theta_{y\quad r} \right)}\frac{l_{r}}{2\left( {l_{f} + l_{r}} \right)}} + {{K_{f}\left( {{{- \theta_{xr}}t_{f}} + {\theta_{y\quad r}l_{f}}} \right)}\cos \left( \theta_{xr} \right)\quad {\cos \left( \theta_{y\quad r} \right)}}}}{{N_{total}(1)} = {{{Ma}_{z}\quad {\cos \left( \theta_{xr} \right)}\quad {\cos \left( \theta_{y\quad r} \right)}\frac{l_{r}}{2\left( {l_{f} + l_{r}} \right)}} + {{K_{f}\left( \quad {{\theta_{xr}t_{f}} + {\theta_{y\quad r}l_{f}}} \right)}{\cos \left( \theta_{xr} \right)}\quad {\cos \left( \theta_{y\quad r} \right)}}}}{{N_{total}(2)} = {{{Ma}_{z}\quad {\cos \left( \theta_{xr} \right)}\quad {\cos \left( \theta_{y\quad r} \right)}\frac{l_{f}}{2\left( {l_{f} + l_{r}} \right)}} + {{K_{r}\left( {{{- \theta_{xr}}t_{r}} - {\theta_{y\quad r}l_{r}}} \right)}{\cos \left( \theta_{xr} \right)}\quad {\cos \left( \theta_{y\quad r} \right)}}}}{{N_{total}(3)} = {{{Ma}_{z}\quad {\cos \left( \theta_{xr} \right)}\quad {\cos \left( \theta_{y\quad r} \right)}\frac{l_{f}}{2\left( {l_{f} + l_{r}} \right)}} + {{K_{r}\left( {{\theta_{xr}t_{r}} - {\theta_{y\quad r}l_{r}}} \right)}{\cos \left( \theta_{xr} \right)}\quad {\cos \left( \theta_{y\quad r} \right)}}}}} & (26)\end{matrix}$

[0126] If in case the heave motion of the vehicle is negligible, i.e.,the heave acceleration of the vehicle is small. Then the verticalacceleration sensor output should be close to the gravity, i.e.

α_(z)≈g  (27)

[0127] In this case an approximation of the normal loadings can bewritten as the following $\begin{matrix}{{{N_{total}(0)} \approx {{{Mg}\frac{l_{r}}{2\left( {l_{f} + l_{r}} \right)}} + {K_{f}\left( {{{- \theta_{xr}}t_{f}} + {\theta_{y\quad r}l_{f}}} \right)}}}{{N_{total}(1)} \approx {{{Mg}\frac{l_{r}}{2\left( {l_{f} + l_{r}} \right)}} + {K_{f}\left( {{\theta_{xr}t_{f}} + {\theta_{y\quad r}l_{f}}} \right)}}}{{N_{total}(2)} \approx {{{Mg}\frac{l_{f}}{2\left( {l_{f} + l_{r}} \right)}} + {K_{r}\left( {{{- \theta_{xr}}t_{r}} - {\theta_{y\quad r}l_{r}}} \right)}}}{{N_{total}(3)} \approx {{{Mg}\frac{l_{f}}{2\left( {l_{f} + l_{r}} \right)}} + {{K_{r}\left( {{\theta_{xr}t_{r}} - {\theta_{y\quad r}l_{r}}} \right)}.}}}} & (28)\end{matrix}$

[0128] The calculated normal loadings provide an indication of wheellift above. When the normal load is near zero, this provides anindication of wheel lift. The normal loads are thus compared to a normalload threshold. When the normal loads are lower (below the threshold) ornear zero, the wheel has lifted. The normal loadings may also be used tocompute the road torques described below.

Wheel Lift Using Road Torque

[0129] The roll condition or wheel lift can also be identified bychecking the actual road torques applied to the wheels and the roadtorques which are needed to sustain the wheels when the wheels aregrounded. The actual road torques can be obtained through torquebalancing for each wheel using wheel acceleration, driving torque andbraking torque. If the wheel is contacting the road surface, thecalculated actual road torques must match or be larger than thenonlinear torques calculated from the normal loading and thelongitudinal slip at each wheel.

[0130] The actual road torques τ_(road) applied to the wheel togetherwith the driving torque τ_(d), braking torque τ_(d) and the wheelrotation inertia I_(w) obey the following Newton's law $\begin{matrix}{{{I_{wf}{\frac{\quad}{t}\left\lbrack \frac{{WhlSpd}(0)}{R_{0f}} \right\rbrack}} = {{\tau_{d}(0)} - {\tau_{b}(0)} - {\tau_{road}(0)}}}{{I_{wf}{\frac{\quad}{t}\left\lbrack \frac{{WhlSpd}(1)}{R_{0f}} \right\rbrack}} = {{\tau_{d}(1)} - {\tau_{b}(1)} - {\tau_{road}(1)}}}{{I_{wr}{\frac{\quad}{t}\left\lbrack \frac{{WhlSpd}(2)}{R_{0r}} \right\rbrack}} = {{\tau_{d}(2)} - {\tau_{b}(2)} - {\tau_{road}(2)}}}{{I_{wr}{\frac{\quad}{t}\left\lbrack \frac{{WhlSpd}(3)}{R_{0r}} \right\rbrack}} = {{\tau_{d}(3)} - {\tau_{b}(3)} - {{\tau_{road}(3)}.}}}} & (29)\end{matrix}$

[0131] Using equations (23), (29) the road torques may be calculated in$\begin{matrix}{{{\tau_{road}(0)} \approx {{\tau_{d}(0)} - {\tau_{b}(0)} - {I_{wf}\frac{s_{r}(0)}{R_{0_{f}}}}}}{{\tau_{road}(1)} \approx {{\tau_{d}(1)} - {\tau_{b}(1)} - {I_{wf}\frac{s_{r}(1)}{R_{0_{f}}}}}}{{\tau_{road}(2)} \approx {{\tau_{d}(2)} - {\tau_{b}(2)} - {I_{wr}\frac{s_{r}(2)}{R_{0_{r}}}}}}{{\tau_{road}(3)} \approx {{\tau_{d}(3)} - {\tau_{b}(3)} - {I_{wr}\frac{s_{r}(3)}{R_{0_{r}}}}}}} & (30)\end{matrix}$

Road Torque when the Wheel is Grounded

[0132] If the wheel is grounded, i.e., contacting the road surface, thenthe grounded road torque T_(road-grd)(i) is related to the wheel slipratio s(i), the wheel side slip angle α(i) and the wheel dynamic normalloading N_(total)(i) through a nonlinear functional relationship as inthe following

τ_(road-grd)(i)=N _(total)(i)φ(s(i), α(i)).  (31)

[0133] A linearization for the nonlinear function φ(,) could beobtained as the following

φ(s(i), α(i))=κ(α(i))s(i)  (32)

[0134] If the wheel side slip angle is small, equation (30) could beapproximated as the following

τ_(road-grd)(i)≈κ(i)N _(total)(i)s(i)  (33)

[0135] where κ(i) is the initial slope of the function κ(α(i)). Theapproximation (33) can be implemented as in the following for (i = 0; i< 4; i + +) { if ( s(i) ≦ 0 & & s(i) ≧ p_BRAKING_LIN_SLIP || s(i) ≧ 0 && s(i) ≦ p_DRIVING_LIN_SLIP ) { τ_(road-grd)(i) = N_(total)(i) *p_SLIP_TO_RT_GAIN * s(i) * R₀; } else if ( s(i) ≦ p_BRAKING_LIN_SLIP ) {τ_(road-grd)(i) = N_(total)(i) * p_SLIP_TO_RT_GAIN *p_BRAKING_LIN_SLIP * R₀; } else { τ_(road-grd)(i) = N_(total)(i) *p_SLIP_TO_RT_GAIN * p_DRIVING_LIN_SLIP * R₀; } }

[0136] where p_BRAKING_LIN_SLIP (for example, −10%) is a braking slipthreshold and p_DRIVING_LIN_SLIP (for example, 25%) is a driving slipthreshold. The thresholds are the maximum slip when the linearrelationship between road torque and the slip are valid during brakingand driving cases.

[0137] As can be seen by the above logic, if during braking the slipratio is less than or equal to zero and the slip ratio is greater thanor equal to a braking slip threshold, or during driving the slip rate isgreater than or equal to zero and the slip rate is less than or equal tothe driving slip threshold, the road torque can be determined by one ofthe three formulas.

[0138] The following is a list of the output variables of the passivewheel lift detector 58. As can be seen, the output has a plurality oflevels. Each one of the wheel lift determinations may generate an outputvariable or state as will be described below. In some instances thestates are characterized in a numerical sense with “absolutely grounded”being the highest value and “no indication” as the lowest value.

Output Variables

[0139] Passive wheel lift status: PWLD(i).

[0140] If the ith wheel is absolutely grounded, thenPWLD(i)=ABSOLUTELY_GROUNDED

[0141] If the ith wheel is in the edge of grounding,PWLD(i)=POSSIBLY_GROUNDED

[0142] If the ith wheel is absolutely lifted, thenPWLD(i)=ABSOLUTELY_LIFTED

[0143] If the ith wheel is in the beginning of liftingPWLD(i)=POSSIBLY_LIFTED

[0144] If the ith wheel's status cannot be firmly identified,PWLD(i)=NO_INDICATION

[0145] The following parameters are used in the determination of wheellifting status.

Parameters

[0146] p_MAX_DRR: the upper bound for dynamic rolling radius. In thisexample a value of (1000 m) was used.

[0147] p_MAX_WDA: the upper bound for the rolling radius based wheeldeparture angle. In this example a value of (13 deg) was used.

[0148] p_ROLL_TH_(—)05=0.05* ROLL_GRADIENT

[0149] p_ROLL_TH_(—)25=0.25* ROLL_GRADIENT

[0150] p_ROLL_TH_(—)40=0.40*ROLL_GRADIENT

[0151] p_ROLL_TH_(—)55=0.55*ROLL_GRADIENT

[0152] p_ROLL_TH_(—)75=0.75*ROLL_GRADIENT

[0153] p_STAT_NLOAD_F: the static normal loading of the front wheels(per wheel).

[0154] p_STAT_NLOAD_R: the static normal loading of the rear wheels (perwheel).

[0155] p_SLIP_RT_GAIN: the gain used to convert slip ratio to normalizedroad torque. In this example a value of (6) was used.

[0156] p_NLOAD_LOSS: the allowed percentage of normal loading loss. Inthis example a value of (0.3) was used.

[0157] p_GRD_DW_DWA_TH: the allowed wheel departure angle for groundeddriven wheel. In this example a value of (0.41 deg) was used.

[0158] p_GRD_NDW_DWA_TH: the allowed wheel departure angle for groundednon-driven wheel. In this example a value of (1.25 deg) was used.

[0159] p_LFT_DW_DWA_TH: the min wheel departure angle for groundeddriven wheel to lift. In this example a value of (4 deg) was used.

[0160] p_LFT_NDW_DWA_TH: the min wheel departure angle for groundednon-driven wheel to lift. In this example a value of (10 deg) was used.

[0161] p_GRD_PR_TH: the braking pressure for grounded wheel torquecondition. In this example a value of (6 bar) was used.

[0162] p_LFT_PR_TH: the braking pressure for lifted wheel select-lowtorque condition. In this example a value of (20 bar) was used.

[0163] p_LFT_SP_MIN_TH: the min slip power for possibly groundedcondition. In this example a value of (0.4) was used.

Comparison Logic

[0164] Various comparisons are used by the embodiment to determine thequalitative level or lack thereof of wheel lifting. The passive wheellift detector 58 sets PWLD(i) for i=0, 1, 2, 3, where 0 represents theFL wheel, 1 represents the RL wheel, and 3 represents the RR wheel. IfPWLD(i)=ABSOLUTELY_GROUNDED, then the ith wheel is definitely contactingthe road surface; if PWLD(i)=POSSIBLY_GROUNDED, then the ith wheel isabout to contact the road surface; if PWLD(i)=ABSOLUTELY_LIFTED then theith wheel is definitely lifted or up in the air; ifPWLD(i)=POSSIBLY_LIFTED, then the ith wheel is about leaving contactingthe road surface; if PWLD(i)=NO_INDICATION, then there is no firmindication for both lifting and grounding for the ith wheel.

[0165] The roll information is first used to screen the grounding andlifting trends of the wheels. The following rough screening uses therelative roll angle θ_(xr) and the roll rate based wheel departure angleθ_(whl). If both the magnitudes of θ_(xr) and θ_(whl) are small, thevehicle wheels are probably grounded: if (θ_(xr) > 0) { if ( θ_(xr) ≦p_ROLL_TH_55 & & θ_(whl) ≦ p_ROLL_TH_05 ) { PWLD(0) = POSSIBLY_GROUNDEDPWLD(2) = POSSIBLY_GROUNDED; } else { PWLD(0) = NO_INDICATION; PWLD(2) =NO_INDICATION; }} else { if ( θ_(xr) ≧ − p_ROLL_TH_55 & &θ_(whl) ≧ −p_ROLL_TH_05 ) { PWLD(1) = POSSIBLY_GROUNDED; PWLD(3) =POSSIBLY_GROUNDED; } else { PWLD(1) = NO_INDICATION; PWLD(3) =NO_INDICATION; } }

[0166] where p_(—ROLL)_TH_(—)05 is the static relative roll anglecorresponding to 5% of the roll gradient, p_ROLL_TH_(—)55 is the staticrelative roll angle corresponding to 55% of the roll gradient. If boththe magnitudes of θ_(xr) and θ_(whl) are large, the vehicle wheels areprobably lifted. After the above first cut, a refinement for determiningabsolutely grounded and absolutely lifted conditions is conducted.

[0167] The first concern is the detection of the absolutely groundedcondition for the wheels. Several variables, including N_(total)(i),τ_(road)(i), τ_(road-grd)(i) and the rolling radii based wheel departureangle θ_(rr-whl)(0), θ_(rr-whl)(1), are used to checking whether the ithwheel is absolutely grounded. Assume that the roll angle screeningthrough logic (35) indicates that the wheels of interest are possiblygrounded. In order to confirm the possibly grounded wheels are actuallyabsolutely grounded, the following conditions are then checked. If anyof those conditions is met, an absolutely grounded flag is set for thewheel of interest.

[0168] Normal loading condition: if PWLD(i)=POSSIBLY_GROUNDED and at thesame time the normal loading satisfies

N _(total)(i)≧Nth(i)

[0169] then PWLD(i)=ABSOLUTELY_GROUNDED. Here four variables N_(th)(i)for i=0, 1, 2, 3 are used as the minimum normal loadings for the wheelswhen they are grounded:

N _(th)(0)=p _(—) STAT _(—) NLOAD _(—) F*(1−p _(—) NLOAD _(—) LOSS);

N _(th)(1)=p _(—) STAT _(—) NLOAD _(—) F*(1−p _(—) NLOAD _(—) LOSS);

N _(th)(2)=p _(—) STAT _(—) NLOAD _(—) R*(1−p _(—) NLOAD _(—) LOSS);

N _(th)(3)=p _(—) STAT _(—) NLOAD _(—) R*(1−p _(—) NLOAD _(—)LOSS);  (36)

[0170] Slip power condition: if PWLD(i)=POSSIBLY_GROUNDED and at thesame time the slip power is negative (s_(p)(i)<0), i.e., the magnitudeof the slip ratio is decreasing (convergent slip ratio), then set thewheel lift flag as PWLD(i)=ABSOLUTELY_GROUNDED.

[0171] Road torque condition: if PWLD(i)=POSSIBLY_GROUNDED and at thesame time the magnitude of the actual road torque τ_(road)(i) from (30)is greater than the grounded wheel road torque τ_(road-grd)(i) from (33)and both have the same sign, or

τ_(road)(i)τ_(road-grd)(i)>=0

and

|τ_(road)(i)|≧|τ_(road-grd)(i)|

[0172] then PWLD(i)=ABSOLUTELY_GROUNDED.

[0173] Active torque condition: if PWLD(i)=POSSIBLY_GROUNDED, and at thesame time the active torque (either braking torque or driving torque)applied to the ith wheel is larger enough while the wheel departureangle generated from rolling radii θ_(rr-whl)(j) for j=0,1 is smallenough, then the ith wheel is deemed to be absolutely grounded. Noticethat the thresholds for driven wheels and non-driven wheels aredifferent.

[0174] The following logic is a summary of the above discussion for thecase where the vehicle is turned left and the left side of the vehiclehas the potential trend to lift up. if θ_(xr) > 0 { if ( PLWD(0) = =POSSIBLY_GROUNDED & &( N_(total)(0) ≧ N_(th)(0) || s_(p)(0) < 0 ||(τ_(road)(0) * τ_(road-grd)(0) ≧ 0 & & | τ_(road)(0) |≧|τ_(road-grd)(0)) ||(|θ_(rr-whl)(0) |≦ p_GRD_DW_DWA_TH & & P_(τ)(0) = = 2& & | τ_(active)(0) |≧ p_GRD_PR_TH * BRKTQ_GAIN_F) ||(θ_(rr-whl)(0) |≦p_GRD_NDW_DWA_TH & & P_(τ)(0)! = 2 & & τ_(active)(0) |≧ p_GRD_PR_TH *BRKTQ_GAIN_F)) ) { PWLD(0) = ABSOLUTELY_GROUNDED; } if ( PLWD(2) = =POSSIBLY_GROUNDED & &( N_(total)(2) ≧ N_(th)(2) || s_(p)(2) < 0||(τ_(road)(2) * τ_(road-grd)(2) ≧ 0 & & | τ_(road)(2) |≧|τ_(road-grd)(2)) ||(|θ_(rr-whl)(1) |≦ p_GRD_DW_DWA_TH & & P_(τ)(2) = = 2& & | τ_(active)(2) |≧ p_GRD_PR_TH * BRKTQ_GAIN_R) ||(θ_(rr-whl)(1) |≦p_GRD_NDW_DWA_TH & & P_(τ)(0)! = 2 & & τ_(active)(2) |≧ p_GRD_PR_TH *BRKTQ_GAIN_R)) ) { PWLD(2) = ABSOLUTELY_GROUNDED; } }

[0175] If the vehicle is turned to the right, then the following logicis used for detecting an absolutely grounded condition if θ_(xr) ≦ 0 {if ( PLWD(1) = = POSSIBLY_GROUNDED & &( N_(total)(1) ≧ N_(th)(1) ||s_(p)(1) < 0 || (τ_(road)(1) * τ_(road-grd)(1) ≧ 0 & & | τ_(road)(1) |≧|τ_(road-grd)(1)) ||(|θ_(rr-whl)(0) |≦ p_DW_DWA_TH & & P_(τ)(1) = = 2 & &| τ_(active)(1) |≧ p_GRD_PR_TH * BRKTQ_GAIN_F) ||(θ_(rr-whl)(1) |≦p_NDW_DWA_TH & & P_(τ)(1)! = 2 & & τ_(active)(1) |≧ p_GRD_PR_TH *BRKTQ_GAIN_F)) ) { PWLD(1) = ABSOLUTELY_GROUNDED; } if ( PLWD(3) = =POSSIBLY_GROUNDED & &( N_(total)(3) ≧ N_(th)(3) || s_(p)(3) < 0||(τ_(road)(3) * τ_(road-grd)(3) ≧ 0 & & | τ_(road)(3) |≧|τ_(road-grd)(3)) ||(|θ_(rr-whl)(1) |≦ p_DW_DWA_TH & & P_(τ)(3) = = 2 & &| τ_(active)(3) |≧ p_GRD_PR_TH * BRKTQ_GAIN_R) ||(θ_(rr-whl)(1) |≦p_NDW_DWA_TH & & P_(τ)(3)! = 2 & & τ_(active)(3) |≧ p_GRD_PR_TH *BRKTQ_GAIN_R)) ) { PWLD(3) = ABSOLUTELY_GROUNDED; } } (38)

[0176] where the torque BRKTQ_GAIN_F and BRKTQ_GAIN_R are two parametersused to convert the braking pressure at the front and rear wheels to thebraking torque applied to the front and rear wheels; p_PRESS_TH denotesthe pressure used to set threshold for active torques.

[0177] Notice that the four variables P_(τ)(i) for i=0, 1, 2, 3 are usedin the logic (38) and (39), which are called the torque patternvariables. P_(τ)(i)s are used to identify the torque patterns where themeaningful wheel lifting information can be identified. This torquepatterning includes positive torques for both left and right side in thefront or the rear axle; negative torques for both left and right side inthe front or the rear axle. In order to eliminate the wheel slipdifference due to significant torque difference between the left andright wheels, the lower of two values is selected. These values are (1)the torque applied to the current wheel of interest, and (2) the torqueapplied to the other wheel on the same axle plus the torque generatedfrom 20 bar of brake pressure

P _(τ)(0)=τ_(active)(0)≦0 & & τ_(active)(1)≦0 &&|τ_(active)(0)|≦|τ_(active)(1)|+p _(—) LFT _(—) PR _(—) TH*BRKTQ _(—)GAIN _(—) F +(τ _(active)(0)>0 & & τ_(active)(1)>0 &&|τ_(active)(0)|≦|τ_(active)(1)|+p _(—) LFT _(—) PR _(—) TH*BRKTQ _(—)GAIN _(—) F)*2;

P _(τ)(2)=τ_(active)(2)≦0 & & τ_(active)(3)≦0 &&|τ_(active)(2)|≦|τ_(active)(3)|+p _(—) LFT _(—) PR _(—) TH*BRKTQ _(—)GAIN _(—) R +(τ _(active)(2)>0 & & τ_(active)(3)>0 &&|τ_(active)(2)|≦|τ_(active)(3)|+p _(—) LFT _(—) PR _(—) TH*BRKTQ _(—)GAIN _(—) R)*2;

P _(τ)(1)=τ_(active)(1)≦0 & & τ_(active)(0)≦0 &&|τ_(active)(1)|≦|τ_(active)(0)|+p _(—) LFT _(—) PR _(—) TH*BRKTQ _(—)GAIN _(—) F +(τ _(active)(1)>0 & & τ_(active)(0)>0 &&|τ_(active)(1)|≦|τ_(active)(0)|+p _(—) LFT _(—) PR _(—) TH*BRKTQ _(—)GAIN _(—) F)*2;

P _(τ)(3)=τ_(active)(3)≦0 & & τ_(active)(2)≦0 &&|τ_(active)(3)|≦|τ_(active)(2)|+p _(—) LFT _(—) PR _(—) TH*BRKTQ _(—)GAIN _(—) R +(τ _(active)(3)>0 & & τ_(active)(2)>0 &&|τ_(active)(3)|≦|τ_(active)(2)|+p _(—) LFT _(—) PR _(—) TH*BRKTQ _(—)GAIN _(—) R)*2;  (39)

[0178] Now the wheels are checked for a lifted condition. Assume theinitial roll information screening as through logic (35) indicates awheel of interest as no indication, then the wheel is probably in thelifting trend. In this case further roll condition screening forpotential lifting is conducted if θ_(xr) > 0 { θ_(cond) = ( θ_(xr) ≧p_ROLL_TH_75 || (θ_(xr) ≧ p_ROLL_TH_50 & & θ_(whl) ≧ p_ROLL_TH_25) ||(θ_(xr) ≧ p_ROLL_TH_40 & & θ_(whl) ≧ p_ROLL_TH_75 )); } else { θ_(cond)= ( θ_(xr) ≦ −p_ROLL_TH_75 || (θ_(xr) ≦ − p_ROLL_TH_50 & & θ_(whl) ≦−p_ROLL_TH_25) || (θ_(xr) ≦ − p_ROLL_TH_40 & & θ_(whl) ≦ − p_ROLL_TH_75)); }

[0179] where p_(—ROLL)_TH_(—)75, p_ROLL_TH_(—)50, p_ROLL_TH_(—)40 andp_ROLL_TH_(—)25 are the static relative roll angle corresponding to 75%,50%, 40% and 25% of the roll gradient. If the above roll screeningcondition θ_(cond)==1, then the first cut for lifting detection isobtained. Notice that the actual wheel departure angle θ_(whl)(calculated from the roll rate sensor) is different from the rollingradius based wheel departure angle θ_(rr-whl)(0) (for front wheels) andθ_(rr-whl)(1) (for rear wheels). As in the grounding wheel detection,further confirmation is needed to obtain absolutely lifted condition.Let PL_(cond)(i) be the possibly lifted flags for the ith wheel, it canbe calculated based on the following two conditions which reflectpossibly lifted conditions:

[0180] Slip power condition: if the slip power of the ith wheels_(p)(i)≧0 indicates that this wheel has a divergent slip ratio, i.e.,the magnitude of the slip ratio is increasing. (Considering potentialnon-braking drag on the wheels, a small negative number is used insteadof 0 is used, i.e., we use s_(p)(i)≧−0.01 to replace s_(p)(i)≧0).

[0181] Normal loading condition: if the ith normal load N_(total)(i) issmaller than a constant threshold, then the ith wheel is possiblylifted;

[0182] For positive relative roll angle, PL_(cond)(0) and PL_(cond)(2)are calculated as in the following if θ_(xr) > 0 { PL_(cond)(0) =s_(p)(0) ≧ −0.01 & &( θ_(cond) = = 1 || N_(total)(0) ≦ p_LOAD_F *p_LOSS); PL_(cond)(2) = s_(p)(2) ≧ −0.01 & &( θ_(cond)= =1 ||N_(total)(2) ≦ p_LOAD_R * p_LOSS); }

[0183] If the relative roll angle θ_(xr) is negative, PL_(cond)(1) andPL_(cond)(3) can be calculated as in the following ifθ_(xr) ≦ 0 {PL_(cond)(1) = s_(p)(1) ≧ −0.01 & &( θ_(cond) = = 1 || N_(total)(1) ≦p_LOAD_F * p_LOSS); PL_(cond)(3) = s_(p)(3) ≧ −0.01 & &( θ_(cond) = = 1|| N_(total)(3) ≦ p_LOAD_R * p_LOSS); }

[0184] Using the calculated condition flags, PL_(cond)(i) will be usedto set possibly lifted status of wheels for (i = 0; i < 4; i + +) { ifPL_(cond)(i) = = 1) PWLD(i) = POSSIBLY_LIFTED; }

[0185] Now the absolutely lifted conditions are determined. In thefollowing we assume the wheels are already in possibly lifted statusthrough (42).

Torque Select-Low Condition for Non-Driven Wheel

[0186] In this case, if the applied braking torque satisfied the torquepattern condition, i.e., for the right loaded wheel case

τ_(active)(left)≧τ_(active)(right)−p _(—) PRES _(—) SL _(—) TH*BRKTQ_(—) GAIN  (44)

[0187] and for left loaded wheel case

τ_(active)(right)≧τ_(active)(left)−p _(—) PRES _(—) SL _(—) TH*BRKTQ_(—) GAIN  (45)

[0188] then the wheel lifting will be checked with the rolling radiusbased wheel departure angle condition for front wheels

|θ_(rr-whl)(0)|≧p _(—) NDW _(—) WDA _(—) TH  (46)

[0189] and for rear wheels

|θ_(rr-whl)(1)|≧p _(—) NDW _(—) WDA _(—) TH  (47)

[0190] where the threshold p_NWD_WDA_TH is the threshold for non-drivenwheel's rolling radius based wheel departure angle.

Torque Select-Low Condition for Driven Wheel During Engine Braking

[0191] In this case torque select-low condition is the same as (29) and(30), but the wheel departure angle conditions needs to use differentthreshold. For right-loaded wheel case

|θ_(rr-whl)(0)|≧p _(—) NDW _(—) WDA _(—) TH  (48)

[0192] and for rear wheels

|θ_(rr-whl)(1)|≧p _(—) NDW _(—) WDA _(—) TH  (49)

Torque Select-Low Condition for Driven Wheel During Engine Driving

[0193] In this case, the torque select-low condition is the same as thefollowing for the right loaded wheel

τ_(active)(left)≧τ_(active)(right)−p _(—) PRES _(—) SL _(—) TH*BRKTQ_(—) GAIN  (50)

[0194] and for left loaded wheel case

τ_(active)(right)≧τ_(active)(left)−p _(—) PRES _(—) SL _(—) TH*BRKTQ_(—) GAIN  (51)

[0195] A detailed logic can be summarized as the following for therighted loaded wheel case: if θ_(xr) > 0 { if (PWLD(0) = = NO_INDICATION& &PWLD(0) = = POSSIBLY_LIFTED) { if ( P_(τ)(0) = = 1 & & θ_(rr-whl)(0)≧ p_LFT_NDW_WDA_TH ||P_(τ)(0) = = 2 & & θ_(rr-whl)(0) ≧ p_LFT_DW_WDA_TH||P_(τ)(0) = = 1 & & θ_(rr-whl)(0) ≧ p_LFT_DW_WDA_TH & & (DRIVE_MODE = =FRONT || DRIVE_MODE = = FOUR || DRIVE_MODE = = TOD) ) ) { PWLD[0] =ABSOLUTELY_LIFTED; } if (s_(p)(0) ≦ − p_LFT_SP_MIN_TH ) { PWLD[0] =POSSIBLY_GROUNDED; } } if (PWLD)2) = = NO_INDICATION & &PWLD(2) = =POSSIBLY_LIFTED) { if (P_(τ)(2) = = 1 & & θ_(rr-whl)(1) ≧p_LFT_NDW_WDA_TH ||P_(τ)(2) = = 2 & & θ_(rr-whl)(1) ≧ p_LFT_DW_WDA_TH||P_(τ)(2) = = 1 & & θ_(rr-whl)(1) ≧ p_LFT_DW_WDA_TH & & (DRIVE_MODE = =FRONT || DRIVE_MODE = = FOUR || DRIVE_MODE = = TOD) ) { PWLD(2) =ABSOLUTELY_LIFT; } if (s_(p)(2) ≦ − p_LFT_SP_MIN_TH) { PWLD(2) =POSSIBLY_GROUNDED; } } }

[0196] Notice that the drive mode is checked in order to distinguishbetween driven wheel engine braking and non-driven wheel braking. If theslip power is negative enough, i.e., the slip ratio has rapid convergentrate, then possibly grounded wheel condition is identified.

[0197] A detailed logic can be summarized as the following for the leftloaded wheel case: if θ_(xr) ≦ 0 { if (PWLD(1) = = NO_INDICATION &&PWLD(1) = = POSSIBLY_LIFTED) { if ( P_(τ)(1) = = 1 & & θ_(rr-whl)(0) ≦−p_LFT_NDW_WDA_TH ||P_(τ)(1) = = 2 & & θ_(rr-whl)(0) ≦ −p_LFT_DW_WDA_TH||P_(τ)(1) = = 1 & & θ_(rr-whl)(0) ≦ −p_LFT_DW_WDA_TH & & (DRIVE_MODE == FRONT || DRIVE_MODE = = FOUR || DRIVE_MODE = = TOD) ) ) { PWLD(1) =ABSOLUTELY_LIFTED; } if (s_(p)(1) ≦ −p_LFT_SP_MIN_TH ) { PWLD(1) =POSSIBLY_GROUNDED; } } if (PWLD(3) = = NO_INDICATION & &PWLD(3) = =POSSIBLY_LIFTED) { if (P_(τ)(3) = = & & θ_(rr-whl)(1) ≦ p_LFT_NDW_WDA_TH||P_(τ)(3) = = 2 & & θ_(rr-whl)(1) ≦ p_LFT_DW_WDA_TH ||P_(τ)(3) = = 1 && θ_(rr-whl)(1) ≦ p_LFT_DW_WDA_TH & & (DRIVE_MODE = = FRONT ||DRIVE_MODE = = FOUR || DRIVE_MODE = TOD) ) { PWLD(3) = ABSOLUTELY_LIFT;} if (s_(p)(3) ≦ − p_LFT_SP_MIN_TH) { PWLD(3) = POSSIBLY_GROUNDED; } } }

[0198] Referring now to FIG. 6, a method for controlling an automotivevehicle as described above is now summarized. In step 70, the vehicleconstants are determined. As described above, various vehicle constantsare used in the present embodiment. The vehicle constants are determinedduring vehicle testing and vary with different suspensions and vehicleconfigurations. Such vehicle constants include suspension resultant rollstiffness K_(roll), roll damping rates D_(roll), the height of thecenter of gravity of the vehicle, the masses of the vehicle includingthe inertial masses which include the roll moments of inertia of thefront and rear wheel tire assemblies around the contact patches of theouter tires, and the total masses of the front and rearwheels/tires/suspension assemblies. In step 72 the various sensors areread. The various sensors may include sensors in FIG. 2. In steps 74-82a first through fifth roll conditions are determined. The conditions mayinclude a relative roll angle and a wheel departure angle calculatedfrom a roll rate sensor and a lateral acceleration sensor, a rollingradius-based wheel departure angle, normal loading at each wheel, anactual road torque and a wheel longitudinal slip. At least threedeterminations are desirable. However, for a more robust system all fiveroll conditions may be determined.

[0199] In step 84 wheel lift in response to the roll conditions aredetermined. In step 86 the rollover control system may be activated tocounter vehicular rolling motion in response to the wheel lift signal.Of course, as described below actuation may be based on a roll anglewhile the wheel lift detection may be used to adjust various parameterssuch as relative roll angle or the road bank angle.

[0200] What has been described above are several different ways in whichto determine wheel lift passively.

Active Wheel Lift Using Change of Torque

[0201] Both passive and active wheel lift detection may be used in arollover control system or other safety system.

[0202] From FIG. 2A above, the command controller 56 may include atorque controller 57 that is used to control the torque of the wheels12A, 12B, 13A, 13B. Torque controller 57 may act in conjunction with theelectronic engine controller, a driveline engagement mechanism orbraking system, or a combination of these to control the torque at oneor all of the wheels 12A, 12B, 13A, 13B. Torque controller 57 and rollcontroller 18 may be coupled to wheel speed sensors 20 located at eachof the wheels. Wheel speed sensors 20 provide roll control system 26with a signal indicative of the speed of the individual wheel to whichit is attached. Various types of wheel speed sensors includingtoothed-wheel type systems would be evident to those skilled in the art.

[0203] In the following active wheel lift example, the application ofbrake pressure is used to provide the change in torque. However, othermethods such as applying engine torque may also be used to change theamount of torque at a wheel. Further references to the application oftorque to a wheel may include hydraulic or electric brake torque,changes in engine torque or engagement of driveline torque through theuse of an electronically controlled transfer case, differential,transmission or clutch. The present embodiment may also be used todetermine if a sensor has failed in the sensor system 16. That is, ifroll is suspected by a particular sensor, but all other conditions orsensors indicate otherwise, the sensor may be operating improperly.Also, although speed is used, wheel acceleration may also be used inplace of speed as would be evident to those skilled in the art.

[0204] Referring now to FIG. 7, the active wheel lift detector 60 isused to perform the following method and generate an active wheel liftsignal. In step 130, if a roll sensor failure is suspected or in step132 if wheel lift is suspected by the roll control system, block 134initiates the wheel lift determination process. In step 136, torque isapplied to the wheel suspected of lifting and the wheel speed at thesuspected wheel is stored. In step 138, the torque is increased byapplying a test pulse of torque to the suspected wheel. Torque isapplied until a torque threshold (Torque_Max) is achieved. In step 140,if the torque is greater than the Torque_Max, the torque is heldconstant in step 142. In step 144, if the time as counted by theBuild_Counter is greater than a predetermined time, step 146 is executedin which the torque is released and the wheel speed at the initiation ofthe release of torque is stored. In step 144, if the counter is notgreater than the predetermined hold time, the counter is incremented instep 148. After step 148 the change in wheel speed is compared to apredetermined change in wheel speed. If the wheel speed change is notgreater than a predetermined speed in step 150, steps 138-144 are againexecuted. If the wheel speed change is greater than a predeterminedspeed, this indicates a lifted wheel. In this case, step 152 is executedin which a wheel lift status flag is set. After step 152, step 154 isexecuted in which the build counter is reset.

[0205] Referring back to step 140, if the torque is not greater than thetorque threshold then step 150 is executed.

[0206] Referring back to step 146, after the wheel speed is recordedafter the torque release, step 156 is executed. In step 156 torque isreleased. After step 156, step 158 is implemented in which the wheelspeed change is compared to a reacceleration threshold. Thereacceleration threshold is a predetermined value that corresponds to awheel speed change that should be achieved should wheel contact bereestablished. The wheel speed change is determined from the time thatthe torque was released. If the wheel speed change is greater than areacceleration threshold or if the wheel lift status from step 152 iszero, wheel contact is assumed. In such a case the traction level may becalculated in step 160. If the wheel speed does not increase over thereacceleration threshold, then the wheel lift status is confirmedbeginning with step 170.

[0207] Referring back to step 158, if the wheel speed is less than thereacceleration threshold, step 162 compares the Dump_Counter to apredetermined dump time. If the predetermined dump time is greater thanthe Dump_Counter, then the Dump_Counter is incremented in step 164 andsteps 156 and 158 are again executed. If the Dump_Counter is greaterthan the predetermined dump time, then the wheel lift status flag is setin step 166 and the Dump_Counter is reset in step 168. After step 168,the process is reinitiated and returns to step 136.

[0208] Returning back to step 160, the traction level is calculated instep 160. After step 160, the plausibility of a sensor failure isdetermined. If, for example, the process was initiated based on thesuspicion of a sensor failure from block 130 above and no wheel lift wasdetected, a sensor failure is indicated in step 172. For either result,if a sensor failure is indicated by block 170 or not, the build counterand Dump_Counter are cleared in block 174 and the wheel lift status iscleared in block 176. The end of the routine occurs in block 178.

[0209] Thus, as can be seen, the application of torque can be used tofirst determine whether a suspected wheel has lifted from the pavement.For confirmation, the removal of the torque and the resulting wheelspeed change may be used to confirm the initial finding. Advantageously,the system may be implemented in a dynamic stability system of anautomotive vehicle without adding further sensors. If rollover isdetected, then the rollover can be corrected by applying the brakes orgenerating a steering correction.

[0210] Referring now to FIG. 8A, various lines 190, 192, 194 areillustrated during the build time to illustrate the variation inpressure of the braking system due to wear and other effects of thebrakes. Lines 190, 192 194 have little effect on the overall operationof the system. Thus, the thresholds and parameters are selected so thatthe system is robust to wear and system variation. The maximum pressurep_(max) is reached and maintained for a hold time (such as set forth instep 42 above) until it is released.

[0211] Referring now to FIG. 8B, a plot of wheel speed corresponding tothe various times is illustrated. As shown, the wheel speed of a loadedwheel is illustrated by line 196, which is higher than the wheel speedof a lifted wheel illustrated by line 198.

Passive Wheel Lift Using Torques

[0212] Referring now to FIG. 9, a passive method similar in theory tothe active method is hereinafter described. That is, rather thanapplying a changing torque to the wheel, an operating input torque tothe wheel may be used. This passive determination may be used in themethod of FIG. 6 described above. Thus, the operating input torque tothe wheel is an unmodified wheel torque from those of the normaloperating conditions in contrast to that described in the parentapplication U.S. Pat. No. 6,356,188, which is incorporated by referenceherein. Consequently, the passive system described below can accommodatethe type of normal operating wheel torque, from low or near zero, tonegative (braking) or positive (accelerating). It should be noted thateach wheel may be subject to this method.

[0213] In step 210, the various sensors in vehicle conditions are read.The following process is performed for each of the wheels. In step 220,the various inputs to the method are obtained and calculated. The inputtorque may be measured by a separate sensor or may be determined usingthe engine torque. The operating input torque to the wheel is a functionof the engine speed, and the distribution of the engine torque to thewheels through a torque transferring system such as a differential anddriveline. Thus, the operating input torque may be determined withoutbeing modified. In contrast to an active system, the active system musthave and generate a change in torque. The slip ratio of each wheel isalso determined. The wheel slip ratio is determined by the difference ofthe wheel speed minus the velocity of the corner divided by the vehiclespeed at the corner. Thus, the wheel slip ratio is a unitless ratio. Thevelocity at each corner of the vehicle may be determined from the wheelspeed sensors described above or may be a function of the yaw rate toaccount for the turning of the vehicle. Thus, the yawing of the vehicleand the speed at the vehicle may be used to determine the vehiclevelocity at the corner of the vehicle.

[0214] In step 220, the wheel acceleration and the slip rate of thevehicle may also be determined. The vehicle slip rate is the change inthe slip ratio described above. That is, the slip ratio derivative isused to determine the slip rate. However, the velocity at each corner ofthe vehicle multiplied by the derivative of the slip ratio may also beused as the slip rate. It has been found in practice that this methodfor determining the slip rate results in a cleaner signal, which isadvantageous in signal processing.

[0215] In step 222, the magnitude and sign (or direction) of the inputtorque is determined. In step 224, if a large magnitude of input torqueis provided (not near zero) step 224 is executed. Step 224 checks thewheel slip ratio. The sign or relative direction of wheel slip ratio andthe magnitude of the wheel slip ratio is compared to thresholds. If thewheel slip ratio is greater than a predetermined magnitude and it hasthe same sign as the input torque, step 226 is executed.

[0216] In step 226, the wheel response is determined. The wheel responsemay be determined using the wheel acceleration, the wheel slip rate, orboth. The wheel response and the wheel slip ratio are compared to athreshold. The threshold may be a function of the input torque. Theterms divergent and convergent are also used. Divergent means that thevalues are trending away from zero, while convergent means the valuesare trending toward zero. In step 226, if the wheel acceleration andslip rate are both divergent and above predetermined correspondingthresholds, step 228 is executed in which a possibly lifted counter isincremented. If this condition holds for a number of cycles, step 230generates a lifted wheel signal indicative that the wheel has lifted.

[0217] In step 230, other vehicle inertial information may be used toconfirm the identity and possibility that the wheel is lifted.

[0218] Referring back to step 226, if the wheel acceleration and/or thewheel slip rate is divergent but below a predetermined threshold, step232 provides no indication to the system. That is, not enoughinformation has been provided.

[0219] In step 226, if the wheel acceleration and the wheel slip rate isconvergent, step 234 is executed. In step 234 a possibly grounded signalis generated and a grounded counter is incremented. In step 236, if theabove condition persists for a predetermined number of cycles, a wheellifted signal is generated for the wheel.

[0220] Referring back to step 224, if the wheel slip is about zero, step238 is executed. In step 238, if the wheel response is below thethreshold, step 234 is executed as described above. The thresholds maybe the same as those described above or may be changed due to the changeof torque. The threshold may also be constant numerical values. If instep 238 the wheel responses are above the thresholds, no information isprovided.

[0221] Referring back to step 224, if the wheel slip ratio has a largemagnitude but has a sign opposite to the input torque, no information isgenerated in step 242.

[0222] Referring back to step 222, if a small input torque near zero isgenerated (the absolute value of the input torque is less than apredetermined input torque) the wheel state is checked in step 244. Instep 244 the magnitude of the wheel slip is determined. If the wheelslip is above a predetermined threshold, the response of the wheel ischecked in step 246. For small torque cases, the wheel response is notlikely to be divergent. However, in this case, lack of convergence maybe used to indicate that the wheel is not grounded. Note that if thewheel does meet the divergence criteria, it also meets thenon-convergent criteria. Thus, if the wheel state is convergent in step246, step 234 is executed. In step 246, if the wheel response isnon-convergent, that is, that significant slip is present and the wheeldoes not have significant acceleration of opposite sign compared to theslip ratio, step 228 is executed. If a smaller input torque and a smallwheel slip is present from step 224, step 248 indicates no information.

[0223] The no information blocks 232, 240, 242, and 248 are all used toprovide no indication of wheel lift. This is because insufficientevidence or conflicting evidence is present.

[0224] One advantage of this passive wheel lift determination is thatthe computations may be run at all times and is generally independent ofthe inertial state information.

Arbitration Between Active and Passive Wheel Lift

[0225] The passive wheel lift detection strategy (PWLD) checks all theavailable motion variables at each time instant to determine if asuspicious wheel is lifted. The advantage of PWLD over AWLD is that theformer could send an indication at each time instant, and the latterneeds to wait a certain period of time before sending out an indication.Another advantage is that during driver braking, PWLD can be usedeffectively to identify wheel lifting. However PWLD, in some cases,suffers a lack of information to determine the wheel lifting status ifthe wheel slip is not disturbed enough and sufficient torque is notpresent.

[0226] Therefore, it is desirable to integrate active and passive wheellift together so as to conduct a reliable wheel lift determination. Thefinal wheel lift status may be used for activating the roll stabilitycontrol system or updating various parameters.

[0227] The passive wheel lift detection (PWLD) system generates thewheel lifting status S_(wld-passive)(i) for the ith wheel, which couldbe any of the following five statuses. The following statuses are setforth in an order from high to low. The statuses may actually beimplemented as a number in the logic of the control scheme. For example“4” may represent absolutely grounded while “0” represents noindication.

[0228] If the ith wheel is absolutely grounded, then

[0229] S_(wld-passive)(i)=ABSOLUTELY_GROUNDED

[0230] If the ith wheel is in the edge of grounding,

[0231] S_(wld-passive)(i)=POSSIBLY_GROUNDED

[0232] If the ith wheel is absolutely lifted, then

[0233] S_(wld-passive)(i) ABSOLUTELY_LIFTED

[0234] If the ith wheel is in the edge of lifting

[0235] S_(wld-passive)(i)=POSSIBLY_LIFTED

[0236] If the ith wheel's status cannot be confirmed, then

[0237] S_(wld-passive)(i)=NO_INDICATION

[0238] As mentioned above there are numerous methods for determiningpassive wheel lift detection for setting S_(wld-passive)(i).

[0239] Active Wheel lift detection, as described above is intended to bean independent means of determining whether a wheel is lifted or not. Byindependent, it is meant that the detection method does not rely on thesignals used to detect the roll state of the vehicle (i.e., roll rateand angle, lateral acceleration, steering wheel angle, vehicle speed,steering wheel angle). Basically, the operation of the algorithm isbroken into a Build Cycle, in which brake pressure is applied to thewheel, and a Release Cycle, in which brake pressure is removed from thewheel. In the Build and Release Cycles, the slip ratio and rate of wheelspeed change is compared to a physical model of a lifted and a groundedwheel, in order to determine the Lift State.

[0240] The intent of the Build cycle is to apply brake pressure to thewheel in order to (i) generate negative slip on the wheel. Typicallyslip ratios less than (more negative than) −15 to −20% are required toassess if a wheel is lifted. Furthermore, slip ratios of this magnitudeare required to assess the Lift State of the wheel in the Release Cycle;(ii) Examine the rate of wheel speed change as a function of brakepressure and engine torque during the build cycle.

[0241] The intent of the Release cycle is to remove brake pressure onthe wheel (Upon Entering Release Initial, the requested pressure on thewheel is set to zero) and (i) examine the rate of wheel speed change asa function of residual brake pressure and engine torque; (ii) Examinethe change in slip ratio as a function of the release counters (i.e.,time in release).

[0242] The active wheel lift detection system generated the wheellifting status S_(wld-active)(i) for the ith wheel.

[0243] A simple arbitration between S_(wld-passive)(i) andS_(wld-active)(i) to provide a final wheel lifting status S_(wld)(i) canbe expressed as in the following for (i = 0; i ≦ 3; i + +) {if(S_(wld-active)(i) = = ABSOLUTELY_GROUNDED) S_(wld)(i) =ABSOLUTELY_GROUNDED; else if(S_(wld-active)(i) = = ABSOLUTELY_LIFTED)S_(wld)(i) = ABSOLUTELY_LIFTED; else if(S_(wld-passive)(i) = =ABSOLUTELY_GROUNDED) S_(wld)(i) = ABSOLUTELY_GROUNDED; elseif(S_(wld-passive)(i) = = ABSOLUTELY_LIFTED) S_(wld)(i) =ABSOLUTELY_LIFTED; else if(S_(wld-active)(i) = = POSSIBLY_GROUNDED)S_(wld)(i) = POSSIBLY_GROUNDED; else if(S_(wld-active)(i) = =POSSIBLY_LIFTED) S_(wld)(i) = POSSIBLY_LIFTED; else if(S_(wld-passive)(i) = = POSSIBLY_GROUNDED) S_(wld)(i) =POSSIBLY_GROUNDED; else if(S_(wld-passive)(i) = = POSSIBLY_LIFTED)S_(wld)(i) = POSSIBLY_LIFTED; else S_(wld)(i) = NO_INDICATION; }

[0244] Although the above simple integration scheme provides an envelopefor both active and passive wheel lifting status, no conflict resolutionis provided. In the logic above, i refers to the wheel number. The frontleft wheel is 0, the front right wheel is 1, the rear left wheel is 2,and the rear right wheel is 3. Thus, wheels 0 and 2 are on the same side(left in this case) of the vehicle while wheels 1 and 3 are on the sameside. (right in this case) of the vehicle. In the above logic, if theactive wheel lift signal is absolutely grounded, the final wheel liftstatus is set to be absolutely grounded. If the above is not true andthe active wheel lift status is absolutely lifted the final wheel liftstatus is set to absolutely lifted. If the above is not true and thepassive wheel lift status is absolutely grounded, then the final wheellift status is absolutely grounded. If the above is not true and thepassive wheel lift status is absolutely lifted then the final wheel liftstatus is set to be absolutely lifted. If the active wheel lift statusis possibly grounded and the above is not true, then the final wheellift status is set to be possibly grounded. If the above is not true andthe active wheel lift status is possibly lifted then the final wheellift status is set to possibly lifted. If the above is not true and thepassive wheel lift status is possibly grounded, then the final wheellift status is said to be possibly grounded. If the above is not trueand the passive wheel lift status is possibly lifted, then the finalwheel lift status is set to be possibly lifted. If any of the above arenot true then the final wheel lift status is set to no indication.

[0245] For example, such an integration does not distinguish between aconflict between S_(wld-passive)(i) and S_(wld-active)(i). The followingconflict removing logic (CRL) which is part of the logic programmed intointegrated wheel lift detector 62 sets the final wheel lifting statusS_(wld)(i) to NO_INDICATION instead of sending out a potentially wrongstatus for (i = = 0; i ≦ 3; i + +) { if( (S_(wld-active)(i) ≦POSSIBLY_GROUNDED & & S_(wld-passive)(i) ≧ POSSIBLY_LIFTED) ||(S_(wld-active)(i) ≧ POSSIBLY_LIFTED & & S_(wld-passive)(i) ≦POSSIBLY_GROUNDED) ) S_(wld)(i) = NO_INDICATION; }

[0246] In the above logic, when the active wheel lift status is lessthan or equal to possibly grounded and the passive wheel lift is greaterthan or equal to possibly lifted for the same wheel, or the active wheellift is greater than or equal to possibly lifted and the passive wheellift signal is less than or equal to possibly grounded then noindication is provided. As can be seen, this logic provides a conflictcheck between the passive wheel lift signal and the active wheel liftsignal for each of the wheels.

[0247] Due to different suspension systems, some vehicle may haveearlier front wheel lifting and a delayed rear wheel lifting; others mayhave rear wheel lifting first and then the front wheel lifting. In thiscase a consistence check for the final wheel lift status can beconducted as in the following CONSISTENCY CHECK LOGIC (CCL). If avehicle has earlier front wheel lifting if( S_(wld)(0) ≦POSSIBLY_GROUNDED & &S_(wld)(2) ≧ POSSIBLY_LIFTED ) { S_(wld)(0) =NO_INDICATION; S_(wld)(2) = NO_INDICATION; } if( S_(wld)(1) ≦POSSIBLY_GROUNDED & &S_(wld)(3) ≧ POSSIBLY_LIFTED ) S_(wld)(1) =NO_INDICATION; S_(wld)(3) = NO_INDICATION; }

[0248] In the above logic, the final wheel lift status for both sides ofthe vehicle are checked. On the left side of the vehicle if the wheellift status of the front wheel is less than or equal to possiblygrounded and the rear wheel is greater than or equal to possibly lifted,both of the final wheel lift statuses for both the front and the rearwheels of the left side of the vehicle are set to no indication. Thesame is true for the right side of the vehicle.

[0249] If a vehicle has earlier rear wheel lifting if( S_(wld)(2) ≦POSSIBLY_GROUNDED & &S_(wld)(0) ≧ POSSIBLY_LIFTED ) { S_(wld)(0) =NO_INDICATION; S_(wld)(2) = NO_INDICATION; } if( S_(wld)(3) ≦POSSIBLY_GROUNDED & &S_(wld)(1) ≧ POSSIBLY_LIFTED ) S_(wld)(1) =NO_INDICATION; S_(wld)(3) = NO_INDICATION; }

[0250] Both the right side of the vehicle and the left side of thevehicle are checked in the above logic. If the final wheel lift statusfor the rear wheel is less than or equal to possibly grounded and thefront left wheel is greater than or equal to possibly lifted, then bothof the front and rear wheel final wheel lift statuses are set to noindication. The same is true for the right side of the vehicle as well.

[0251] If the vehicle relative roll angle is very small and the rollrate signal tries to decrease the relative roll angle, then anotherconsistency check logic (CCL) can be conducted. If the vehicle isturning left if( θ_(xr) ≧ 0 & &θ_(xr) ≦ Θ & &w_(x) ≦ 0 ) { if(S_(wld)(0)≧ POSSIBLY_LIFTED) { S_(wld)(0) = NO_INDICATION; } if(S_(wld)(2) ≧POSSIBLY_LIFTED) { S_(wld)(2) = NO_INDICATION; } }

[0252] In the above logic, if the roll angle is greater than 0 and theroll angle is less than or equal to a threshold, indicative that theroll angle is small, and the roll rate is less than or equal to 0 andthe final wheel lift status of the front left wheel is greater than orequal to possibly lifted, then no indication is provided. Likewise, ifthe final wheel lift status of the left rear wheel is greater than orequal to possibly lifted then no indication is provided. As can be seenby the logic immediately below, the relative roll angle, the thresholdand the roll rate may be used to detect a consistency in the right sideof the vehicle. That is, if the relative roll angle θ_(xr) is less thanor equal to 0 and the relative roll angle is greater than or equal tothe negative relative roll angle threshold and the roll rate is greaterthan or equal to 0, and if the final wheel lift status of the frontright wheel greater than or equal to possibly lifted, no indication isprovided. The same check is performed for the rear wheel.

[0253] If the vehicle is turning right if( θ_(xr) ≦ 0 & &θ_(xr) ≧ −Θ &&w_(x) ≧ 0 ) { if(S_(wld)(1) ≧ POSSIBLY_LIFTED) { S_(wld)(1) =NO_INDICATION; } if(S_(wld)(3) ≧ POSSIBLY_LIFTED) { S_(wld)(3) =NO_INDICATION; } }

[0254] Considering the roll stability control system applies brakingpressure to the front wheels during the initial stage of pressurebuild-up, braking pressure for active wheel lift detection on the otherwheel that shares a brake circuit with the RSC control wheel isterminated so as to guarantee all the brake fluid in the brake circuitwill be used to build control pressure. Hence if the vehicle has afront-rear split braking system, the following pressure inhibit logic(PIL) will be used to turn off active wheel lift detection (AWLD)if(P_(RSC)(0) ≦ P_(est)(0) + Υ) { Turn off AWLD at wheel 1; S_(wld)(1) =S_(wld-passive)(1) } if(P_(RSC)(1) ≦ P_(est)(1) + Υ) { Turn off AWLD atwheel 0; S_(wld)(0) = S_(wld-passive)(0) }

[0255] where P_(RSC)(i) is the rollover stability control system requestbraking pressure at front wheels, P_(est)(i) is the estimated caliperpressure, and Υ is a pressure offset. As can been seen by the abovelogic, if either of the pressure requested by the front wheels is lessthan or equal to an estimated caliper pressure plus an offset, the finalwheel status of either of the front wheels is then set to the passivewheel status. Therefore, the active wheel check for the particular wheelis disabled.

[0256] If the vehicle has a diagonal split braking system, the followingpressure inhibit logic (PIL) will be used to turn off active wheel liftdetection (AWLD). if(P_(RSC)(0) ≦ P_(est)(0) + Υ) { Turn off AWLD atwheel 1; S_(wld)(1) = S_(wld-passive)(1) } if(P_(RSC)(1) ≦ P_(est)(1) +Υ) { Turn off AWLD at wheel 0; S_(wld)(0) = S_(wld-passive)(0) }

[0257] Considering that during driver braking, the torque disturbance isenough to initiate a solid PWLD result, the following driver brakingdetection integration logic (DBDIL) is conducted if(DRIVER_BRAKING_FLAG= = 1 & &P_(driver) ≧ ψ) { Turn off AWLD at wheel i; S_(wld)(i) =S_(wld-passive)(i) }

[0258] where Ψ is a threshold for driver braking pressure P_(driver).

[0259] Thus, as can be seen by the above logic, if the driver or vehicleoperator applies the brakes a braking flag will be generated. If thebrake pressure requested by the driver is above a threshold then activewheel lift is disabled for the wheel. That is, the final wheel status isset to the passive wheel status.

[0260] Considering that during a large driving torque application (forexample, wide open throttle case), there are enough wheel torquedisturbance to initiate a solid PWLD result, the following open throttledetection integration logic (OTDIL) if(OPEN_THROTTLE_FLAG = = 1 &&τ_(driving)(i) ≧ Γ) { Turn off AWLD at wheel i; S_(wld)(i) =S_(wld-passive)(i) }

[0261] where τ_(driving)(i) is the positive driving torque applied tothe ith wheel due to engine torque and Γ is the threshold forτ_(driving)(i).

[0262] As the above logic shows, when the driving torque for aparticular wheel due to engine is compared to a threshold, whichindicates a throttle status such as wide open throttle, the active wheellift detection is disabled. That is, the final wheel lift status Swld isset to the passive wheel lift status.

Angle Corrections from Wheel Lift/Grounded Determination

[0263] Referring now to FIG. 10, the relationship of the various anglesof the vehicle 10 relative to the road surface 11 is illustrated. In thefollowing a reference road bank angle θ_(bank) is shown relative to thevehicle 10 on a road surface. The vehicle has a vehicle body 10 a andwheel axle 10 b. The wheel departure angle θ_(wda) is the angle betweenthe wheel axle and the road. The relative roll angle θ_(xr) is the anglebetween the wheel axle 10 b and the body 10 a. The global roll angleθ_(x) is the angle between the horizontal plane (e.g., at sea level) andthe vehicle body 10 a.

[0264] Another angle of importance is the linear bank angle. The linearbank angle is a bank angle that is calculated more frequently (perhapsin every loop) by subtracting the relative roll angle generated from alinear roll dynamics of a vehicle (see U.S. Pat. No. 6,556,908 which isincorporated by reference herein), from the calculated global roll angle(as the one in U.S. application Ser. No. 09/789,656, which isincorporated by reference herein). If all things were slowly changingwithout drifts, errors or the like, the linear bank angle and referenceroad bank angle terms would be equivalent.

[0265] Referring now to FIG. 11, controller 26 is illustrated in furtherdetail. The controller 26 receives the various sensor signals 20, 28-39.From the various sensor signals wheel lift detection may be determined.The modules described below (and above) may be implemented in hardwareor software in a general purpose computer (microprocessor). From thewheel lift detection module 52, a determination of whether each wheel isabsolutely grounded, possibly grounded, possibly lifted, or absolutelylifted may be determined, as described above. Transition detectionmodule 252 is used to detect when the vehicle is experiencing aggressivemaneuver during a transition turn from the left to right or right toleft. The sensors may also be used to determine a relative roll angle inrelative roll angle module 54. Relative roll angle may be determined inmany ways. One way is to use the roll acceleration module 258 inconjunction with the lateral acceleration sensor (see U.S. Pat. No.6,556,908 incorporated by reference herein) for detail. As describedabove, the relative roll angle may be determined from the rollconditions described above.

[0266] The various sensor signals may also be used to determine arelative pitch angle in relative pitch angle module 256 and rollacceleration in roll acceleration module 258. The outputs of the wheellift detection module 50, the transition detection module 52, and therelative roll angle module 54 are used to determine a wheel departureangle in wheel departure angle module 260. Various sensor signals andthe relative pitch angle in relative pitch angle module 256 are used todetermine a relative velocity total in module 262. The road referencebank angle step 264 determines the bank angle. The relative pitch angle,the roll acceleration, and various other sensor signals as describedbelow are used to determine the road reference bank angle. Other inputsmay include a roll stability control event (RSC) and/or the presence ofa recent yaw stability control event (WLDFlag).

[0267] The global roll angle of the vehicle is determined in global rollangle module 266. The relative roll angle, the wheel departure angle,and the roll velocity total blocks are all inputs to the global rollangle module 266. The global roll angle block determines the global rollangle θ_(x). An output module 68 receives the global roll angle module266 and the road reference bank angle from the road reference bank anglemodule 264. A roll signal for control, which will be directly used ingenerating control command from the feedback control law, is developedin roll signal module 270. The roll signal for control is illustrated asarrow 272. A sensitizing and desensitizing module 74 may also beincluded in the output module 68 to adjust the roll signal for control.

[0268] In the reference road bank angle module 264, the reference bankangle estimate is calculated. The objective of the reference bankestimate is to track the true road bank angle experienced during drivingin both stable and highly dynamic situations. Most importantly, whencompared to the global roll estimate, it is intended to capture theoccurrence and physical magnitude of a divergent roll condition (twowheel lift) should it occur. This signal is intended to be used as acomparator against the global roll estimate for calculating the errorsignal of the roll controller 26.

[0269] The roll signal for control is calculated as the(θ_(x)−θ_(refbank)), i.e., the subtraction of the reference bank anglefrom the global roll angle.

[0270] As mentioned above various errors not limited to integration,calculation and drift may enter into the various signals at varioustimes. Thus, in certain situations the wheel departure angle or thereference bank angle may not be accurate. The following descriptiondescribes how these values can be updated in response to wheellift/wheel grounded values.

[0271] As described above, wheel lift detection includes both detectingthat the wheels are grounded and that the wheels are lifted. Theseconditions are relatively certain and thus may be used to update certaincalculated values such as the reference roll angle and the wheeldeparture angle.

[0272] Referring now to FIG. 12, a high level flow chart illustratingthe condition detection and the resulting actions according to thisembodiment of the present invention is illustrated. In step 300 varioussensors described above are read. In step 302 various method selectionsbased upon the particular drive train are determined. For example, themethod selection may adjust the various factors based upon the presenceand condition of the center differential. This step will be furtherdescribed in FIG. 13.

[0273] In step 304, passive wheel lifting/grounding detection isdetermined. Thereafter, in step 306, a final lifting/grounding conditionarbitration is performed.

[0274] Referring back to step 302, a parallel process to that of step304 is described. In step 308 it is determined whether or not activedetection is required. If active detection is not required step 306 isperformed. If after detection is required, step 310 performs activewheel lift/grounding detection. Thereafter, step 306 arbitrates betweenthe lifting and grounding conditions as described above. The arbitratedcondition for each of the wheels of the vehicle is determined. Afterstep 306, the resulting actions from the wheel lifting/groundingconditions are determined. Step 304 is further described in FIG. 14.Step 310 is further described in FIG. 15 and step 312 is furtherdescribed in FIG. 16.

[0275] As shown in step 268 of FIG. 11, the roll signal for control isultimately determined. The roll signal for control is a function of theglobal roll angle and the reference roll angle. The reference bank anglemay also be adjusted in response to the wheel departure angle and therelative roll angle generated from a linear roll dynamics model as willbe further described below.

[0276] Referring now to FIG. 13, step 320 describes whether a centerdifferential is engaged. If the center differential is engaged in step320, step 322 determines whether or not this engagement is feasible orrequired. If the disengagement is not feasible or required then step 328selects an averaging method for the two sides of the vehicle.

[0277] When the vehicle is in 4×4 mode, the front and rear axles arecoupled through the driveshaft. This drivetrain coupling results in anunknown front/rear torque split and causes transient oscillations of thewheels. These factors prevent an accurate evaluation of lift for eachwheel end, but lift can still be evaluated by treating the wheels oneach side of the vehicle as a two-wheel system. By considering alltorques on the two-wheel system and looking at the overall systemresponse, a method analogous to the individual wheel method can be usedto detect lift.

[0278] For each side of the vehicle, the two-wheel system response isdetermined by averaging the responses of the front and rear wheels onthat side. The key change for 4×4 wheel lift detection is that theaverage wheel speeds and slip values (front averaged with rear for eachside of the vehicle) are used instead of values for each individualwheel. The lift is evaluated for each side of the vehicle instead ofevaluating each wheel. By the above a robust identification location oftwo wheel lift is determined. Single wheel life may be identified onlywhen there is a sufficiently low amount of loading on the second wheel.

[0279] In step 322 if the disengagement is feasible and required, step324 disengages the center differential. Thereafter, step 326 isperformed. Step 326 is also performed if the center differential is notengaged in step 320. An individual method is used in step 326. That is,individual method selects the individual wheels of the front or rear ofthe vehicle.

[0280] Referring now to FIG. 14, step 304 above is described in furtherdetail. The grounding/lifting conditions described below may bedetermined within the wheel lift detection module. In step 330, thegrounding condition is screened. If the grounding condition isdetermined in step 330, the passive wheel grounding condition detectoris set. That is, the passive wheel lift being absolutely grounded isdetermined. In step 334, the passive detection arbitration logicreceives the absolutely grounded condition for the wheel. In parallel,the lifting condition is screened in step 336. In step 336, if liftingcondition is passively detected in step 338 the output is provided topassive detection arbitration logic 334. In steps 330 and 336, if anabsolutely grounded or absolutely lifting condition is not determined,the AND block of step 340 is used to form a no indication detector instep 342. After step 342 the passive detection arbitration logic 334provides a final passive detection signal. The output of the passivedetection arbitration logic 334 is an absolutely lifted condition,possibly lifted condition, an absolutely grounded condition, a possiblygrounded condition, or a no indication detector. The no indicationdetector is generated when the conditions are not absolutely or possiblytrue. That is, the conditions other than the aforementioned fourconditions will be deemed as no indication.

[0281] Referring now to FIG. 15, step 350 generates an active torquecontrol. Steps 352, 354 and 356 corresponded to the logic describedabove. That is, step 352 determines active wheel grounding in responseto the active torque provided in step 350. In step 354 active wheel liftis detected and in step 356 a no indication detector is provided. Instep 358, the no indication detector is conducted when the conditionsare not absolutely or possibly true. The detection arbitration logic instep 358 thus provides an absolutely grounded condition, an absolutelylifted condition, possibly grounded condition, possibly lifted conditionor a no indication for each of the wheels.

[0282] Referring now to FIG. 16, step 312 is illustrated in furtherdetail. In step 312, the terminology illustrated on the figures is asfollows: FI is the front inside wheel of the turn, RI is the rear insidewheel of the turn, AG is an absolutely grounded flag, NI indicates noindication, AL indicates absolutely lifted, and WDA is the wheeldeparture angle. The front inside wheel and the rear inside wheel referto the position of the wheels while making a turn. Thus, in a left handturn the front inside wheel would be the left front wheel whereas theleft rear wheel would be the rear inside wheel. In a right hand turn thefront inside wheel is the front right wheel whereas the rear insidewheel is the rear right wheel.

[0283] In steps 360 and 362 the front inside wheel and the rear insidewheel are determined whether or not they are absolutely grounded. If oneor the other is absolutely grounded step 364 is executed. Thus, ifeither one of the front inside wheel or the rear inside wheel isabsolutely grounded, step 368 is executed. In step 368 the referencebank angle is ramped down toward the linear bank angle. Although onesingle adjustment could be made, in a control system it may be desirableto gradually increment the reference bank angle to the linear bankangle. This logic is true because the linear bank angle which iscalculated more often than the reference bank angle is a more accuraterepresentation of the road bank than the reference bank angle when atleast one of the front or rear inside wheels is absolutely grounded.After step 368, step 314 of FIG. 12 is executed. In step 370 it isdetermined whether the front inside wheel is absolutely grounded or thefront outside wheel is outside is less than or equal to a no indicationstatus. Less than or equal to no indication status indicates absolutelyor possibly grounded. In step 372 it is determined the right insidewheel is absolutely grounded and if the rear outside wheel is less thanor equal to no indication. The outputs of steps 370 and 372 are providedto an OR gate 374. Thus, if either of the conditions in steps 370 and372 are true, then it is determined whether or not the system is in atransition maneuver in step 376. A transition maneuver refers to whenthe system is transitioning or turning from left to right or right toleft. If a transition maneuver is not present in step 376, the step 378is executed. In step 378 the estimated lateral acceleration generatedfrom the steering wheel angle is determined. If such an estimatedlateral acceleration magnitude is less than a threshold, step 380 isexecuted in which the wheel departure angle is set to zero. Thus, thewheel departure angle should not be greater than zero when the system isabsolutely grounded.

[0284] Referring back to steps 370 and 372, the outputs of these stepsare also provided to an AND gate 382. If each of these conditions istrue then the wheel departure angle is set to zero in step 380. Afterstep 380, step 314 is executed from FIG. 12. In step 390 the frontinside wheel and rear inside wheel are determined if they are absolutelylifted. If these wheels are absolutely lifted the sum of the wheeldeparture angle and αθ_(xr) is subtracted from the reference bank angle.The α refers to a boost factor which, in this example, is 1.1. Bysubtracting this number from the reference bank angle, the roll signalfor control angle is increased. This is desirable in a system so that anabsolutely lifted condition increases the amount of control provided bythe system. If the condition in step 390 is not true, the step 394 isexecuted. In step 394 if either the front inside wheel is absolutelylifted or the rear inside wheel is absolutely lifted, step 396 isexecuted in which the wheel departure angle alone is subtracted from thereference bank angle. Thus, this indicates that some increase and theroll signal for control is provided. After step 396, step 314 from FIG.12 is executed. In step 398 if the front inside wheel is absolutelylifted and the rear inside wheel is not absolutely grounded or the rearinside wheel is absolutely lifted and the front inside wheel is notabsolutely grounded, step 400 is executed. In this situation the wheellift screening condition may stop checking the wheel lifting condition.Therefore, the wheel departure angle is continued or initiated in thisstep to provide some hysteresis in the wheel lifting detection.

[0285] Thus as can be seen, the roll signal for control may be adjustedaccording to the wheel lift/wheel grounded conditions.

[0286] While particular embodiments of the invention have been shown anddescribed, numerous variations and alternate embodiments will occur tothose skilled in the art. Accordingly, it is intended that the inventionbe limited only in terms of the appended claims.

What is claimed is:
 1. A system for an automotive vehicle having a wheelcomprising: a first roll condition detector generating a first rollcondition signal; a second roll condition detector generating a secondroll condition signal; a third roll condition detector generating athird roll condition signal; and determining wheel lift in response tothe first roll condition, the second roll condition and the third rollcondition.
 2. A system as recited in claim 1 wherein first rollcondition, said second roll condition and said third roll condition aredetermined passively.
 3. A system as recited in claim 1 wherein saidcontroller generates a passive wheel lift status signal.
 4. A system asrecited in claim 1 wherein said passive wheel lift status signalcomprises a plurality of levels.
 5. A system as recited in claim 1wherein said controller generates a potential rollover signal inresponse to the wheel lift signal.
 6. A system as recited in claim 5further comprising a safety device, said controller controlling saidsafety device in response to said potential rollover signal.
 7. A systemas recited in claim 6 wherein said safety comprises at least one of anactive brake control system, an active rear steering system, an activefront steering system, an active anti-roll bar system, and an activesuspension system.
 8. A method for controlling an automotive vehiclehaving an axle and wheels comprising: determining a first rollcondition; determining a second roll condition; determining a third rollcondition; and generating a wheel lift status signal in response to thefirst roll condition, the second roll condition and the third rollcondition.
 9. A method as recited in claim 8 wherein determining thefirst roll condition comprises: measuring a roll rate; measuring avehicle lateral acceleration; and determining a relative roll angle inresponse to the vehicle roll rate and the vehicle lateral acceleration.10. A method as recited in claim 9 further comprising determining awheel departure angle in response to the vehicle roll rate and thevehicle lateral acceleration.
 11. A method as recited in claim 8 whereindetermining a second roll condition comprises determining a rollingradius-based wheel departure roll angle.
 12. A method as recited inclaim 8 wherein determining a third roll condition comprises determininga normal loading at each wheel.
 13. A method as recited in claim 8further comprising determining a fourth roll condition and whereindetermining a wheel lift comprises determining a wheel lift in responseto the first roll condition, the second roll condition, the third rollcondition and the fourth roll condition.
 14. A method as recited inclaim 8 wherein determining a fourth roll condition comprisescalculating an actual road torque.
 15. A method as recited in claim 8further comprising determining a fifth roll condition and whereindetermining a wheel lift comprises determining a wheel lift in responseto the first roll condition, the second roll condition, the third rollcondition, the fourth roll condition and the fifth roll condition.
 16. Amethod as recited in claim 15 wherein determining comprises determininga fifth roll condition comprises determining a wheel longitudinal slip.17. A method of controlling a vehicle having a plurality of wheelscomprising: determining a relative roll angle; determining a wheeldeparture angle; determining a rolling radius-based wheel departureangle; determining normal loading at each wheel; determining an actualroad torque; determining a wheel longitudinal slip; and determining awheel lift status for said plurality of wheels in response to saidrelative roll angle, said wheel departure angle, said rollingradius-based wheel departure roll angle, the normal loading at eachwheel, an actual road torque and the wheel longitudinal slip.
 18. Amethod as recited in claim 17 wherein determining a relative roll anglecomprises measuring a roll rate; measuring a vehicle lateralacceleration; and determining the relative roll angle in response to avehicle roll rate and the vehicle lateral acceleration.
 19. A method asrecited in claim 17 wherein determining a wheel departure anglecomprises: measuring a roll rate; measuring a vehicle lateralacceleration; and determining the wheel departure angle in response to avehicle roll rate and the vehicle lateral acceleration.
 20. A method asrecited in claim 17 wherein determining a rolling radius-based wheeldeparture angle comprises: measuring a wheel speed; determining a wheellinear velocity; and determining the rolling radius-based wheeldeparture angle in response to the wheel speed and the wheel linearvelocity.
 21. A method as recited in claim 17 wherein determining normalloading at each wheel comprises determining a heave and non-heave loadat each of the plurality of wheels.
 22. A method as recited in claim 17wherein determining an actual road torque comprises determining adriving torque, determining a braking torque and determining a wheelrotation inertia.
 23. A method as recited in claim 17 whereindetermining a wheel longitudinal slip comprises determining a slip powerand a slip rate, and wherein determining a wheel lift status comprisedetermining a wheel lift status for said plurality of wheels in responseto said relative roll angle, said wheel departure angle, said rollingradius-based wheel departure roll angle, the normal loading at eachwheel, an actual road torque, the wheel longitudinal slip, said slippower and said slip rate.
 24. A method for controlling an automotivevehicle having a plurality of wheels comprising: determining a firstwheel lift condition; determining a second wheel lift condition;determining a third wheel lift condition; and generating a wheel liftflag in response to the first wheel lift condition, the second wheellift condition and the third wheel lift condition.
 25. A method asrecited in claim 24 wherein generating a wheel lift flag comprisesgenerating a wheel lift flag for each of the plurality of wheels.
 26. Amethod as recited in claim 24 further comprising comparing the firstwheel lift condition to a first threshold; comparing the second wheellift condition to a second threshold; comparing the third wheel liftcondition to a third threshold; wherein generating a wheel lift flagcomprises generating a wheel lift flag is performed in response tocomparing the first wheel lift condition to a first threshold, comparingthe second wheel lift condition to a second threshold, and comparing thethird wheel lift condition to a third threshold.
 27. A method ofcontrolling an automotive vehicle having a first wheel and a secondwheel having a common axis comprising: determining a first wheel speed;determining a first linear corner velocity of the wheel; determining afirst rolling radius of the wheel as a function of the wheel speed andlinear corner velocity; and controlling a safety system in response tothe first rolling radii.
 28. A method as recited in claim 27 furthercomprising: determining a longitudinal slip ratio; comparing the slipratio to a slip ratio threshold; and performing determining a firstrolling radius when the longitudinal slip ratio is below the slip ratiothreshold.
 29. A method as recited in claim 27 wherein determining alinear corner velocity comprises determining a linear corner velocity asa function of a side slip angle and a vehicle reference velocity.
 30. Amethod as recited in claim 27 wherein determining a linear cornervelocity comprises determining a linear corner velocity as a function ofa steering wheel angle and a vehicle reference velocity.
 31. A method asrecited in claim 27 wherein determining a linear corner velocitycomprises determining a linear corner velocity as a function of a sideslip angle, steering wheel angle, and a vehicle reference velocity. 32.A method as recited in claim 27 further comprising determining a secondrolling radii corresponding to the second wheel.
 33. A method as recitedin claim 32 further comprising determining a wheel departure angle as afunction of the first rolling radii and the second rolling radii.
 34. Amethod of controlling an automotive vehicle having a first wheel, asecond wheel comprising: determining a wheel speed; determining avehicle speed; determining a linear corner velocity of the wheel as afunction of the vehicle speed; determining a first rolling radius of thefirst wheel as a function of the wheel speed and the linear cornervelocity; determining a rolling radius wheel departure angle as afunction of the first rolling radius; generating a wheel lift signal inresponse to the rolling radius departure angle; and controlling a safetysystem in response to the wheel lift signal.
 35. A method for passivelydetermining wheel lift of a wheel of an automotive vehicle comprising:determining a wheel speed; determining a linear corner velocity of thewheel; determining a rolling radius of the wheel as a function of thewheel speed and linear corner velocity; determining a rolling radiuswheel departure angle as a function of the rolling radius; anddetermining a wheel lift condition as a function of the operating inputtorque, the rotational speed of the wheel and the wheel response.
 36. Amethod for controlling an automotive vehicle comprising: determining aslip power for a wheel; determining convergence or divergence of theslip power; generating a wheel lift signal in response to divergence ofthe slip power; and controlling a safety system in response to the wheellift signal.
 37. A method as recited in claim 36 further comprisinggenerating a wheel grounded signal in response to convergence of theslip power.
 38. A method as recited in claim 36 wherein the slip poweris a function of a slip ratio.
 39. A method as recited in claim 38wherein determining a slip ratio is determined as a function of wheelspeed and the vehicle velocity.
 40. A method as recited in claim 39wherein determining a slip ratio is determined as a function of wheelspeed, yaw rate and the vehicle velocity.
 41. A method of controlling anautomotive vehicle comprising: determining a slip ratio; determining aslip power in response to the slip ratio; when the slip power ispositive, generating a wheel lift signal; and controlling a safetysystem in response to the wheel lift signal.
 42. A method as recited inclaim 41 further comprising when the slip power is negative, generatinga wheel grounded signal.
 43. A method as recited in claim 41 furthercomprising controlling a safety system in response to the wheel groundedsignal.
 44. A method as recited in claim 41 wherein determining a slippower comprises determining the slip power in response to the slip ratioand a time derivative of the slip ratio.
 45. A method as recited inclaim 41 wherein determining a slip ratio is determined as a function ofwheel speed and the vehicle velocity.
 46. A method as recited in claim41 wherein determining a slip ratio is determined as a function of wheelspeed, yaw rate and the vehicle velocity.
 47. A system for an automotivevehicle having a safety system comprising: a plurality of wheel speedsensor generating a plurality of wheel speed signals including a firstwheel speed signal; a vehicle velocity generator generating a vehiclevelocity signal; and a controller coupled to said wheel speed sensor andthe vehicle velocity generator, said controller determining a slip ratioin response to the wheel speed signal and the vehicle velocity signal,said controller determining a slip power in response to the slip ratio,when the slip power is positive, said controller generating a wheel liftsignal and said controller controlling the safety system in response tothe wheel lift signal.
 48. A system as recited in claim 47 wherein theplurality of wheel speed signals are used to generate the vehiclevelocity signal.
 49. A system as recited in claim 47 further comprisinga yaw rate sensor generating a yaw rate signal, said slip ratio being afunction of the yaw rate signal.
 50. A method for controlling anautomotive vehicle comprising: determining a slip rate for a wheel;comparing the slip rate to a threshold; generating a wheel lift signalin response to slip rate when the slip rate is above a threshold; andcontrolling a safety system in response to the wheel lift signal.
 51. Amethod as recited in claim 50 further comprising generating a wheelgrounded signal in response to slip rate.
 52. A method as recited inclaim 50 wherein the slip rate is a function of a slip ratio.
 53. Amethod as recited in claim 52 wherein determining a slip ratio isdetermined as a function of wheel speed and the vehicle velocity.
 54. Amethod as recited in claim 52 wherein the slip rate is a function of thetime derivative of the slip ratio.
 55. A method as recited in claim 52wherein determining a slip ratio is determined as a function of wheelspeed, yaw rate and the vehicle velocity.
 56. A method of controllingautomotive vehicle comprising: determining a slip rate; generating awheel lift signal in response to slip rate; and controlling a safetysystem in response to the wheel lift signal.
 57. A method as recited inclaim 56 further comprising generating a wheel grounded signal inresponse to slip rate.
 58. A method as recited in claim 57 furthercomprising controlling a safety system in response to the wheel groundedsignal.
 59. A method as recited in claim 56 wherein determining a sliprate comprises determining the slip rate in response to a velocity and atime derivative of a slip ratio.
 60. A method as recited in claim 59wherein determining a slip ratio is determined as a function of wheelspeed and the vehicle velocity.
 61. A method as recited in claim 59wherein determining a slip ratio is determined as a function of wheelspeed, yaw rate and the vehicle velocity.
 62. A system for an automotivevehicle having a safety system comprising: a plurality of wheel speedsensor generating a plurality of wheel speed signals including a firstwheel speed signal; a vehicle velocity generator generating a vehiclevelocity signal; and a controller coupled to said wheel speed sensor andthe vehicle velocity generator, said controller determining a slip ratioin response to the wheel speed signal and the vehicle velocity signal,said controller determining a slip rate in response to the slip ratio,when the slip rate is above a threshold, said controller generating awheel lift signal and said controller controlling the safety system inresponse to the wheel lift signal.
 63. A system as recited in claim 62wherein the plurality of wheel speed signals are used to generate thevehicle velocity signal.
 64. A system as recited in claim 62 wherein theplurality of wheel speed signals are used to generate a corner velocitysignal, wherein the slip rate is a function of the corner velocitysignal
 65. A system as recited in claim 63 further comprising a yaw ratesensor generating a yaw rate signal, said slip ratio being a function ofthe yaw rate signal.
 66. A method of controlling an automotive vehiclecomprising: determining a heave normal load and a non-heave normal load;determining a total normal load as a function of the heave normal loadand non-heave normal load; generating a wheel lift signal in response tothe total normal load; and controlling a safety system of an automotivevehicle in response to the wheel lift signal.
 67. A method as recited inclaim 66 wherein the heave normal load is a function of a verticalacceleration.
 68. A method as recited in claim 66 wherein the heavenormal load is a function of a roll angle.
 69. A method as recited inclaim 68 wherein the roll angle is a relative roll angle.
 70. A methodas recited in claim 68 wherein the roll angle is a function of rollrate.
 71. A method as recited in claim 66 wherein the heave normal loadis a function of a vertical acceleration and a relative roll angle. 72.A method as recited in claim 66 wherein the heave normal load is afunction of pitch angle.
 73. A method as recited in claim 72 wherein thepitch angle is a relative pitch angle.
 74. A method as recited in claim72 wherein the pitch angle is a function of a pitch rate.
 75. A methodas recited in claim 66 wherein the heave normal load is a function of avertical acceleration, relative roll angle and pitch angle and a vehiclemass.
 76. A method as recited in claim 66 wherein the non-heave normalload is a function of a vertical acceleration.
 77. A method as recitedin claim 66 wherein the non-heave normal load is a function of rollangle.
 78. A method as recited in claim 77 wherein the roll angle is arelative roll angle.
 79. A method as recited in claim 77 wherein theroll angle is a function of roll rate.
 80. A method as recited in claim66 wherein the non-heave normal load is a function of a verticalacceleration and relative roll angle.
 81. A method as recited in claim66 wherein the non-heave normal load is a function of pitch angle.
 82. Amethod as recited in claim 81 wherein the pitch angle is a relativepitch angle.
 83. A method as recited in claim 81 wherein the pitch angleis a function of a pitch rate.
 84. A method as recited in claim 66wherein the non-heave normal load is a function of a verticalacceleration, relative roll angle and pitch angle and a spring rate ofthe vehicle mass.
 85. A method of controlling a vehicle having a wheeland suspension comprising: determining a pitch angle; determining a rollangle; determining a vertical acceleration; determining a normal loadingdue to a heave motion in response to pitch angle, roll angle, verticalacceleration and a mass of the vehicle; determining a normal loading dueto non-heave motion in response to pitch angle, roll angle, verticalacceleration and a spring rate of the suspension; determining a totalnormal load as a function of the normal loading due to the heave motionand a normal load due to non-heave motion; generating a wheel liftsignal in response to the total normal load; and controlling a safetysystem of an automotive vehicle in response to the wheel lift signal.86. A method as recited in claim 85 wherein the roll angle is a relativeroll angle.
 87. A method as recited in claim 85 wherein the roll angleis a function of roll rate.
 88. A method as recited in claim 85 whereinthe pitch angle is a relative pitch angle.
 89. A method as recited inclaim 85 wherein the pitch angle is a function of a pitch rate.
 90. Asystem for controlling an automotive vehicle having a wheel, asuspension and a safety system comprising: a pitch rate sensorgenerating a pitch rate signal; a vertical acceleration sensor; a rollrate sensor generating a roll rate signal; and a controller coupled tothe vertical acceleration sensor, the roll rate sensor and the pitchrate sensor, said controller determining a roll angle from the roll ratesignal and a pitch angle from the pitch angle signal, said controllerdetermining normal loading due to a heave motion in response to pitchangle, roll angle, vertical acceleration and a mass of the vehicle, saidcontroller determining a normal loading due to non-heave motion inresponse to pitch angle, roll angle, vertical acceleration and a springrate of the suspension, said controller determining a total normal loadas a function of the normal loading due to the heave motion and a normalload due to non-heave motion, said controller generating a wheel liftsignal in response to the total normal load, and said controllercontrolling the safety system of an automotive vehicle in response tothe wheel lift signal.
 91. A system as recited in claim 90 wherein theroll angle is a relative roll angle.
 92. A system as recited in claim 90wherein the pitch angle is a relative pitch angle.
 93. A method ofcontrolling an automotive vehicle having a wheel comprising: determiningan actual road torque applied to the wheel; determining a calculatedroad torque; and generating a wheel lift signal in response to thecalculated road torque and the actual road torque.
 94. A method asrecited in claim 93 wherein determining an actual road torque comprisesdetermining an actual road torque as a function of wheel acceleration.95. A method as recited in claim 93 wherein determining an actual roadtorque comprises determining an actual road torque as a function ofwheel acceleration and driving torque.
 96. A method as recited in claim93 wherein determining an actual road torque comprises determining anactual road torque as a function of wheel acceleration and brakingtorque.
 97. A method as recited in claim 93 wherein determining anactual road torque comprises determining an actual road torque as afunction of wheel acceleration, driving torque and braking torque.
 98. Amethod as recited in claim 93 wherein determining a calculated roadtorque comprises determining a calculated road torque in response tonormal loading.
 99. A method as recited in claim 93 wherein determininga calculated road torque in response to normal loading comprisesdetermining a heave normal load and a non-heave normal load, anddetermining a total normal load as a function of the heave normal loadand non-heave normal load.
 100. A method as recited in claim 93 whereindetermining a calculated road torque comprises determining a calculatedroad torque in response to normal loading and longitudinal wheel slip.101. A method of controlling an automotive vehicle comprising:determining a braking torque; determining a driving torque; determininga wheel acceleration; determining an actual road torque as a function ofwheel acceleration, driving torque and braking torque; determining atotal normal load; determining a calculated road torque in response tothe total normal load; comparing the actual road torque and thecalculated road torque; when the actual road torque is less than thecalculated road torque, generating a wheel lift signal; and controllinga safety device in response to the wheel lift signal.
 102. A method asrecited in claim 101 wherein determining a total normal load comprisesdetermining a heave normal load and a non-heave normal load, anddetermining a total normal load as a function of the heave normal loadand non-heave normal load.
 103. A method as recited in claim 101 whereindetermining a total normal load as a function of the heave normal loadand non-heave normal load comprises determining a heave load in responseto pitch angle, roll angle, vertical acceleration and a mass of thevehicle.
 104. A method as recited in claim 101 wherein determining atotal normal load as a function of the heave normal load and non-heavenormal load comprises determining a non-heave load as a function ofpitch angle, roll angle, vertical acceleration and a spring rate of asuspension
 105. A method as recited in claim 101 wherein determining acalculated road torque comprises determining a calculated road torque inresponse to normal loading a longitudinal wheel slip.
 106. A method forcontrolling an automotive vehicle having a plurality of wheelscomprising: measuring a yaw rate; determining a lateral acceleration;determining a roll rate; determining longitudinal acceleration;generating wheel lift signal as a function of yaw rate, lateralacceleration, roll rate and longitudinal acceleration; and controlling asafety system in response to the wheel lift signal.
 107. A method asrecited in claim 106 further comprising determining a pitch accelerationand, wherein determining wheel lift comprises determining wheel lift asa function of yaw rate, lateral acceleration, roll rate, longitudinalacceleration and pitch acceleration.
 108. A method as recited in claim106 further comprising controlling the safety system to counteract wheellift.